Question

The number of ants in a colony was 50 in 1996 and has increased by 14% each year. Which exponential growth model shows the number of aunts in the colony in terms of t, the number of years since 1996?

Answer 1

Solution:

Given that;

The number of ants in a colony was 50 in 1996 and has increased by 14% each year.

The formula for exponential growth is

$\begin{gathered} f(t)=a(1+r)^t \\ Where \\ \text{a is the initial amount} \\ \text{r is the growth rate} \\ t\text{ is number of years since 1996 } \end{gathered}$

Where

$\begin{gathered} a=50 \\ r=\frac{14}{100}=0.14 \end{gathered}$

Substitute the values of the variables, a and r into the exponential growth formula above

$\begin{gathered} f(t)=50(1+0.14)^t=50(1.14)^t \\ f(t)=50(1.14)^t \end{gathered}$

Hence, the equation that models the exponential growth is

$f(t)=50(1.14)^{t}$