In 2000, the population of Israel was approximately 6.27 million and by 2040 it is projected to grow to 9 million. Use the exponential growth model:A=A_o. e^ (kt) in which t is the number of years after 2000, to find an exponential growth function that models the data.

A = (6.27*10^6). e^ (0.009t)

Step-by-step explanation:

Exponential growth model,

A = Ao. e^ (kt)

In 2000, the population of Israel is 6.27 million or 6.27*10^6

The question set the t, as the time in year starting 2000

i. e. at t = 0, Ao = 6.27*10^6

In 2040, the population is projected to grow to 9 million or 9*10^6.

In this year, t=40 because it is 40 year after the projected as t=0 (in 2000).

Substitute the t = 40 and A=9*10^6

9*10^6 = (6.27*10^6). e^ (40k)

e^ (40k) = 9/6.27 = 1.435

40k = ln (1.435) (here we do natural log for both left and right side)

40k = 0.36

k = 0.009

Therefore, the growth function is

A = (6.27*10^6). e^ (0.009t)