Question

The population in Smalltown in 2010 was 56,382 people and is growing exponentially at a rate of 1.2 percent. Which of the following equations defines the population t years after 2010?A) P=56,382e1.2tB) P=56,382e0.012tC)P=56,382( 1 + 0.12)tD)p=56,382( 1 + 0.012)t

Answer 1

Exponential growth happens when an initial population increases by the same percentage or factor over equal time increments or generations. Given the percentage r, and the initial population P0, the equations that defines the model has the following form:

`P(t)=P_0(1+(r)/(100))^t`

Using our known values, the equation for our problem is:

`P(t)=56,382(1+0.012)^t`