word problem for college algebra

Question

Chicago's population grew from 2.8 million in 1990 to 2.9 million in 2000.


(a) What was the yearly percent growth rate?

Round your answer to three decimal places.

The yearly percent growth rate was

.

(b) Assuming the growth rate continues unchanged, what population is predicted for 2025?

Round your answer to three decimal places.

The population of Chicago is predicted to be ___
million in 2025.

Answer 1

Liz,

The equation for a constant rate of growth is P = P₀(1+r)^t, where r is the decimal growth rate and t is the time in years.

 

So with the given information we get:         1.9 = 1.8(1+r)¹⁰

 

solving for r:    2.9/2.8 = (1+r)¹⁰

                       tenthroot(2.9/2.8) = 1+r

                       tenthroot(2.9/2.8) - 1 = r

                       .00352 = r     so the % growth rate is 0.352%

 

b) for P₂₀₂₅ in millions we use:  P₂₀₂₅ = 2.8(1.00352)³⁵ = 3.166 million