9 In 2016 we estimated that around 20 million students would

9. In 2016, we estimated that around 20 million students would attend American colleges and universities. Suppose that the projection for the year 2026 is that 30 million students will attend Let f be the finction that assigns, to each year after 2016, the estimated number of students attending American colleges and universities a. Find a formula for f. Assume f is exponential. b. Estimate how many students will attend American colleges universities in 2021 c. If we assume the exponential growth trend carries into the past as well, try to estimate the number of students attending American colleges universities in 2015.

Solution

Exponential Growth function :

f(n) = foe^bn

So, n =0 is year 2016 and n = 10 is year 2026

We have two points to solve the exponential equation:

( 0, 20 mill) and ( 10, 30 mill)

So, f(n) = 20e^bn

30 = 20e^10b

ln1.5 = 10b

b = ln1.5/10 = 0.0405

a) So, f(n) = 20e^(0.0405n)

b) Year 2021 means n = 5

f(5) = 20e^(0.0405*5) = 20*1.224 = 24.489 = 24.48 million

c) in 2015 ; n = -1

So, f(-1) = 20e^(0.0405*-1) = 19.206 = 19.21 million