Question

Question

In the last 6 years, the population of San Francisco has grown at a rate of 1.26% per year to 870,887. If this rate continues,
what will be the population in 5 more years? Round your answer to the nearest whole number.

Answer 1

927,518

Explanation:

Answer 2

`927,154\ people`

Explanation:

we have a exponential function of the form

`y=a(b^x)`

where

y is the population of San Francisco

x is the number of years

a is the initial population

b is the base

r is the rate of grown

b=(1+r)

In this problem we have

`r=1.26\%=1.26/100=0.0126`

`b=1+0.0126=1.0126`

ordered pair (6, 870,887)

substitute in the exponential function
`y=a(b^x)`

`870,887=a(1.0126^6)`

Solve for a

`a=870,887/(1.0126^6)`

`a=807,857\ people`

so

The exponential function is equal to

`y=807,857(1.0126^x)`

In 5 more years the number of years will be equal to

6+5=11 years

For x=11 years

substitute the value of x in the exponential function and solve for y

`y=807,857(1.0126^(11))`

`y=927,154\ people`