Question
Find the average rate of the function g(x)= 1/4 * 2^x over the interval 3≤x≤7.
a. 7.5
b. 10
c. 15
d. 30
a. 7.5
b. 10
c. 15
d. 30
Answers
GPT 3.5
To find the average rate of the function g(x)= 1/4 * 2^x over the interval 3≤x≤7, we need to find the difference in function values at the endpoints and divide by the difference in x-values.
First, let's plug in the given endpoints into the function:
g(3) = 1/4 * 2^3 = 1/4 * 8 = 2
g(7) = 1/4 * 2^7 = 1/4 * 128 = 32
Next, we find the difference in function values:
32 - 2 = 30
Finally, we find the difference in x-values:
7 - 3 = 4
To find the average rate, we divide the difference in function values by the difference in x-values:
Average rate = (30)/(4) = 7.5
Therefore, the average rate of the function g(x)= 1/4 * 2^x over the interval 3≤x≤7 is 7.5.
Therefore, the correct answer is option a) 7.5.
First, let's plug in the given endpoints into the function:
g(3) = 1/4 * 2^3 = 1/4 * 8 = 2
g(7) = 1/4 * 2^7 = 1/4 * 128 = 32
Next, we find the difference in function values:
32 - 2 = 30
Finally, we find the difference in x-values:
7 - 3 = 4
To find the average rate, we divide the difference in function values by the difference in x-values:
Average rate = (30)/(4) = 7.5
Therefore, the average rate of the function g(x)= 1/4 * 2^x over the interval 3≤x≤7 is 7.5.
Therefore, the correct answer is option a) 7.5.