Question

if the population of a state is 1,821,000 and is decreasing by 0.2% every year. What will the population be in 5 years? Round to the nearest whole number.​

Answer 1

The answer is 182100, because you multiply .2 by 5 which gives us .10, you then multiply .10 by 1,821,000, giving us 182100

Answer 2

1,802,863

Step-by-step explanation:

Initial population of state = 1,821,000

Decay rate = 0.2% = 0.002

Time = 5 years

The exponential decay function is

`f(t)=a(1-r)^t`

where, a is initial value, r is decay rate and t is time in years.

Substitute a=1,821,000 and r=0.002 in the above function.

`f(t)=1,821,000(1-0.002)^t`

`f(t)=1,821,000(0.998)^t`

The population function is
`f(t)=1,821,000(0.998)^t`.

Substitute t=5 in the above function.

`f(5)=1,821,000(0.998)^5`

`f(5)=1802862.69447`

`f(5)\approx 1802863`

Therefore, the population after 5 years is 1,802,863.