Question

The population of new york city increased from 8,192,426 in 2010 to 8,550,405 in 2015 the annual rate of population increase for the period was about 0.9%

A. write an equation for the population t in years after 2010


B. use the equation to predict the population of new york city in 2025

Answer 1

Part A)
`y=8,192,426(1.009)^t`

Part B)
`9,370,872\ people`

Explanation:

we know that

The equation of a exponential growth function is equal to

`y=a(1+r)^t`

where

y is the population

t is the number of years since 2010

a is the initial value

r is the rate of change

we have

`a=8,192,426\\r=0.9\%=0.9\100=0.009`

substitute

`y=8,192,426(1+0.009)^t`

`y=8,192,426(1.009)^t`

Part B) use the equation to predict the population of New York city in 2025

Find the value of t

t=2025-2010=15 years

substitute the value of t in the exponential equation

`y=8,192,426(1.009)^(15)=9,370,872\ people`