A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare
over the interval-2≤x≤0?
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The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
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Comparing the behaviors of both functions, we can conclude that the exponential function decays at the same rate as the quadratic function over the interval -2 ≤ x ≤ 0.
To compare the decay rates of the quadratic function and the exponential function over the interval -2 ≤ x ≤ 0, we need to analyze the behavior of each function within that range. A quadratic function is represented by an equation in the form of f(x) = [tex]ax^2[/tex] + bx + c, where a, b, and c = constants.
The graph of a quadratic function is a parabola. If the coefficient 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards. On the other hand, an exponential function is represented by an equation in the form of f(x) = a * [tex]b^x[/tex], where 'a' and 'b' are constants, and 'b' is the base of the exponential function.
The graph of an exponential function is a curve that either increases or decreases exponentially, depending on the value of 'b'. To compare the decay rates of the two functions, we need to examine their behavior over the given interval. If the exponential function is decaying at a slower rate than the quadratic function, it means its values are decreasing at a lesser rate.
In the case of the quadratic function, if 'a' is negative, the parabola opens downwards, and its values decrease as x increases. Therefore, the quadratic function is decaying in this interval. For the exponential function, since it is not explicitly stated whether it is increasing or decreasing, we can assume that it is decreasing if 'b' is between 0 and 1. In that case, as x increases, the exponential function decays.
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what is secondary economic activity in geography
Answer:by adding raw materials-
Explanation:
add value to the raw materials by changing their form, or combining them into useful and hence more valuable commodity.
John loves to sleep late in the morning. He also knows that school is important. This morning, John chose
to wake up and get to school on time. In doing this, he gave up the opportunity to sleep in. The opportunity cost
of John's choice to go to school is two or three hours of sleep.
Ana loves to go camping with her family and is looking forward to their trip next weekend. Ana learns that her
good friend is having a sleepover birthday party the same Saturday as the trip.
For Ana, what would be the opportunity cost of going to her friend's party? Why?
Answer:
Explanation:
The opportunity cost for Ana of going to her friend's party would be missing out on the camping trip with her family. In this scenario, Ana has to make a choice between attending her friend's party or going on the camping trip. By choosing to attend the party, Ana gives up the opportunity to spend time with her family and enjoy the camping experience. The camping trip, with its potential for family bonding and outdoor activities, represents the alternative option that Ana sacrifices when she decides to attend the party. Therefore, the opportunity cost for Ana is the enjoyment and experience she would have gained from the camping trip.