Equations of Exponential Functions


A 30-gram sample of bacteria has some unknown disease that is killing the bacteria. The amount of bacteria is measured each day and the results are shown in the table.


What is the amount of bacteria on the 8th day?


a. On the eighth day, the bacteria is 1.72 grams

b. On the eighth day, the bacteria is 19.90 grams

c. On the eighth day, the bacteria is 6.23 grams

d. On the eighth day, the bacteria is 6271.89 grams


Please select the best answer from the choices provided

As determined in part, the ball reaches its highest point at time t is 2 seconds

S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.

The ball's starting speed is 64 feet per second.

(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).

(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.

(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.

v(t) = 32 - 16t = 0

or 16t = 32

out = 2 seconds.

As determined in part, the ball reaches its highest point at t = 2 seconds (c).

s(t = 2) = 32(2) - 16(2) (2)

2

or 32 feet if s(t = 2).

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Answer:

-729

Step-by-step explanation:

sequence is to multiply by -3 to get next term

Answer: C 1 - 5i

Step-by-step explanation:

1 is real part graphed sideways

- 5i is imaginary part (that’s what the i means)

And is graphed up and down

Answer: 102

Step-by-step explanation:

Let the numbers be a, a+2 and a+4. Since the sum of three consecutive even numbers is 312, this will be:

a + a+2 + a+4 = 312

3a + 6 = 312

3a = 312 - 6

3a = 306

a= 306/3

a = 102

Therefore, the smallest number is 102.

Other numbers are 104 and 106.

Answer:

3

Step-by-step explanation:

divide 12 by 4 and then multiply that number by 1

Answer:

3

Step-by-step explanation:

3 Because 4 = 1 and if its 12 then u have to divide it by 4 which is 3 also can u tell me if i got it right casue if its wrong im really sorry but im 99.99999999% sure its 3 lol

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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Answer:

9. m(YZ) = 102°

10. m(JKL) = 192°

11. m<GHF = 75°

Step-by-step explanation:

9. First, find the value of x

4x + 3 = 3x + 15 (inscribed angle that are subtended by the same arc are equal based on the inscribed angle theorem)

Collect like terms

4x - 3x = -3 + 15

x = 12

4x + 3 = ½(m(YZ)) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Plug in the value of x

4(12) + 3 = ½(m(YZ))

48 + 3 = ½(m(YZ))

51 = ½(m(YZ))

Multiply both sides by 2

51*2 = m(YZ)

102 = m(YZ)

m(YZ) = 102°

10. First, find the value of x.

7x + 5 + 6x + 6 = 180° (opposite angles in an inscribed quadrilateral are supplementary)

Add like terms

13x + 11 = 180

13x = 180 - 11

13x = 169

x = 169/13

x = 13

7x + 5 = ½(m(JKL)) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Plug in the value of x

7(13) + 5 = ½(m(JKL))

96 = ½(m(JKL))

Multiply both sides by 2

2*96 = m(JKL)

m(JKL) = 192°

11. First, find x.

5x + 15 = ½(11x + 18) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Multiply both sides by 2

2(5x + 15) = 11x + 18

10x + 30 = 11x + 18

Collect like terms

10x - 11x = -30 + 18

-x = -12

Divide both sides by -1

x = 12

m<GHF = 5x + 15

Plug in the value of x

m<GHF = 5(12) + 15

m<GHF = 60 + 15

m<GHF = 75°

Answer:

1. a quantity that stands alone and is not changed by other quantities. most often x variable.

2. a quantity that changes depending on another quantity, as a result of the rule. most often the y variable

Step-by-step explanation:

Answer: A quantity that stands alone and is not changed by other quantities most often X variable.

A quantity that changes depending on another quantity, as a result of the rule most often Y variable.

Answer:

30.6km/h

Step-by-step explanation:

To change from m/s to km/h needs to multiple by 36/10

36/10 × 8.5

=30.6km/h

Answer: 1040

Step-by-step explanation:

just took 65 and mutiply 65$

Answer:

Step-by-step explanation:

Answer:

you'll know bc your fridge will be broken

Step-by-step explanation:

Answer:

When there is footprints in the butter.

Step-by-step explanation:

Answer:

The 95% confidence interval for the true proportion of businesses owned by women is (0.2763, 0.4037).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of businesses in a particular state found that out of 150 surveyed, 51 were owned by women.

This means that [tex]n = 150, \pi = \frac{51}{150} = 0.34[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.34 - 1.96\sqrt{\frac{0.34*0.66}{150}} = 0.2763[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.34 + 1.96\sqrt{\frac{0.34*0.66}{150}} = 0.4037[/tex]

The 95% confidence interval for the true proportion of businesses owned by women is (0.2763, 0.4037).

Answer:

  y < 1/2x +6

Step-by-step explanation:

You want the inequality graphed in the given figure.

The line is dashed, and the shading is below it, so the inequality will have the form ...

  y < ...

This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.

The y-intercept is at +6, where the line crosses the y-axis.

The line goes 2 units to the right for each 1 unit up, so its slope is ...

  m = rise/run = 1/2

The slope-intercept equation for the boundary line is ...

  y = mx +b . . . . . . slope m; y-intercept b

  y = 1/2x +6 . . . . . equation of the boundary line in the graph

Putting the boundary line expression into the inequality form gives the inequality that describes the graph:

  y < 1/2x +6

Answer: hello the list related to your question is missing hence i will give you a general answer that will enable to pick the correct option from the list you have.

answer :

The correct number from the list that corresponds to the null hypothesis will be a number ≥ P - value / critical value

The correct number form the list that corresponds to the alternate hypothesis will be a number ≤ P - value / critical value

Step-by-step explanation:

Determine the null and alternative hypothesis

Mean difference = 0.914

standard deviation = 1.496

duration of test = 2 days

n ( sample size ) = 40

assuming  99% confidence interval

critical value = 2.708 ( using excel function : TINV (0.01, 40 - 1 ) )

Given that the aim of the experiment is to determine the effect of alcohol on driving ability

H0 : μ : Impairs driving

Ha : μ : does not impair driving

Note :

when the P-value is  ≤ significance level we reject the Null hypothesis

while when the P-value is ≥ significance level we reject the alternate hypothesis

The correct number from the list that corresponds to the null hypothesis will be a number ≥ P - value / critical value

The correct number form the list that corresponds to the alternate hypothesis will be a number ≤ P - value / critical value

==============================================

Explanation:

40% + 35% = 75% of the coins were either made before 1940, or made from 1940 to 1980. In other words, 75% of the coins were minted before 1980. This leaves 100% - 75% = 25% of the coins to being minted after 1980.

25% of 1600 = 0.25*1600 = 400 coins were made after 1980

Answer:

6/11

Step-by-step explanation:

24/4=6

44/4=11

Answer:

6/11

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

151

Step-by-step explanation:

Answer:

152 miles

Step-by-step explanation:

There are 2 Xs above 20 1/2, so she rode that distance twice. There are 3 Xs above 22 1/2, so she rode that distance three times. The other distances with Xs she only did once. We add up the distances for each X to get the total:

20.5 + 20.5 + 21.5 + 22 + 22.5 + 22.5 + 22.5 = 152 miles

Answer:

I usually turn the fractions into a decimal. So it would turn into

.666 < x< .777

When you turn your answers into fractions, the only one that fits is C which is 3/4 or .75

Step-by-step explanation:

Answer:

answer in link

Step-by-step explanation

alekscgi/x/Isl.exe

Answer:

b = -8

Step-by-step explanation:

To determine the value of b, we can use the factoring method. We can factor the expression

(5b + 16)(b + 32) as (b + 8)(5b + 16).

Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.

Solving for b in the first equation, we get b = -8.

Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.

This equation is true only when the value of b is -8. Therefore, the value of b is -8.

1/x^7

Step-by-step explanation:

To the 7th power is positive. It's the first one.

Hope this helps, have a good day!

it is A because X is unknown u can put 0 as a denominator so it 1 the X is still unknown and your exponents are 0

Answer:

11.2

Step-by-step explanation:

We can use the pythagorean theorem to find b.

the formula is as follows:

a^2 + b^2 = c^2

We are given a is 10 and c is 15, so we can plug those two numbers in:

10^2 + b^2 = 15^2

Now, we can simplify and solve:

100 + b^2 = 225

b^2 = 125

b = √125

√125 is about 11.1803398875, and to the nearest tenth, this rounds to:

11.2

Answer:

254.47

Step-by-step explanation:

A= 3.14 x r²

A = 3.14 x 9

A = 254.47

Hope this helps

Answer

254.3—- rounded

A= Pi times r squared - this is formula for area of circle

area=  3.14 Times 9 squared

3.14 times 81

254.3

make sure to substitute values!

I hope this helps!

Answer:

y = 5

Step-by-step explanation:

Because of the perpendicular bisector, we know that WZ is congruent to WX. Therfore, we can set their equations as equal to eachother and solve for y.

Answer:

-1/3

Step-by-step explanation: