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: $P=1.4(0.88)^t$

Step-by-step 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.