The population of a city is modeled by the function y = 35000(0.94) {}^(t)where y is the population of the city after t years starting in the year 2000.what is the approximate p…

Question

The population of a city is modeled by the function
`y = 35000(0.94) {}^(t)`where y is the population of the city after t years starting in the year 2000.what is the approximate population of the city in the year 2012? (round to the nearest person)

Answer 1

The given function is

`y=35000(0.94)^t`

y is the population

t is the time since the year 2000

We need to find the population in the year 2012

To find t subtract 2000 from 2012

`t=2012-2000=12`

Substitute t by 12 in the function above

`\begin{gathered} y=35000(0.94)^(12) \\ y=16657.21102 \end{gathered}`

Round it to the nearest whole number

`y=16657`

The population is about 16657 in the year 2012