Question

In 1990, the population of the U.S. was approximately 250 million and was expected to grow according to the function P(x)=250,000,000e⁰.⁰⁰⁹ˣ ,where x is the number of years after 1990. What will the expected U.S. population be in 2010, according to this model?

a) 275 million
b) 300 million
c) 325 million
d) 350 million

Answer 1

The expected U.S. population in 2010, according to the given model, is approximately 296 million.

Step-by-step explanation:

To find the expected U.S. population in 2010 according to the given model, we need to substitute the value of x = 20 into the function P(x). The model is given as P(x) = 250,000,000e^(0.009x), where x is the number of years after 1990. Therefore, P(20) = 250,000,000e^(0.009*20).

Using a calculator to evaluate the right side of the equation, we get P(20) ≈ 295.9234 million. Rounding to the nearest million, the expected U.S. population in 2010 according to this model is approximately 296 million (option b).