# The population of the US was 203 million in the year 1970 and 249 million in the year 1990. If it is growing exponentially, what will it be in the year 2030?

Jun 2, 2016

375 millions, nearly.

#### Explanation:

Let the population Y years from 1970 be P millions.

For exponential growth, the mathematical model will be

P=A B^Y$. When Y = 0, P = 203. So, $203 = A {B}^{0} = A \left(1\right) = A$. Referred to Y= 0 in 1970, Y in 1990 is 20 and P then was 249... So, 249=203 B^20$. Solving, B=(249/203)^(1/20)=1.0103, nearly

Therefore, $P = 203 {\left(\frac{249}{203}\right)}^{\frac{Y}{20}}$

Now, in 2030, Y = 60, and so, P = 203(1.0103)^60

$= 375$ millions, rounded to 3-sd.