Use the table of integrals to find the average value of the growth function over the interval ,where N is the size of a population and t is the time in days.Round your answer to three decimal places.
A) 1280.000
B) 3037.844
C) 1279.773
D) 2816.025
E) 2816.057

Question

Use the table of integrals to find the average value of the growth function  over the interval  ,where N is the size of a population and t is the time in days.Round your answer to three decimal places. ​
A) 1280.000 
B) 3037.844 
C) 1279.773 
D) 2816.025 
E) 2816.057

Quizplus · Accepted Answer

The average value of a function f(x) over the interval [a,b] is given by:

$(1/(b-a)) * \int_{a}^{b} f(x) dx $

In this case, we need to find the average value of the growth function over the interval [0, 20]. Using the table of integrals, we find that:

$\int e^{kt} dt = (1/k) * e^{kt} + C$

where k is a constant.

So,

$1/(20-0) * \int_{0}^{20} N*e^{0.1t}dt$

= $1/2 * (N/(0.1))* (e^{0.1*20} - e^{0.1*0})$

= $1279.773N$

Rounding this to three decimal places, we get the answer as C: 1279.773.

Use the Table of Integrals to Find the Average Value