Question

The population of Austinburg on January 1, 2000 was 1.4 million. the population has decreased at a rate of 12% each year since. which equation models the population (in millions), p, of Austinburg t years after january 1, 2000

Answer 1

Answer:
`P=1.4(0.88)^t`

Explanation:

The exponential equation to show decay in population :

`P=P_0(1-r)^t` (i) , where P= population after t years,
`P_0` = initial population, r =rate of decay.

Given: The population of Austinburg on January 1, 2000 :
`P_0=1.4\text{ million}`

r= 12%= 0.12

Put theses values in (i), we get

`P=1.4(1-0.12)^t\\\\\Rightarrow\ P=1.4(0.88)^t`, which gives the population (in millions), p, of Austinburg t years after January 1, 2000.