Question

The graph shows information about the lion population at a safari park.In 2012, the park has a population of 32 lions. A year later, in 2013, the park has 128 lions. Write an exponential function that models this situation. The lions are growing at a rate of 4 (common ratio). Let xrepresent the number of years since 2010 and let yrepresent the number of lions.a. What was the initial number of lions in the park?b. Write an equation to represent the scenario.

Answer 1

a.

The equation will be given by:

$y=y_o(4)^x$

Where:

yo = Initial amount

The initial amount can be found using the data provided:

$\begin{gathered} x=2,y=32 \\ 32=y_o(4)^2 \\ 32=16y_o \\ y_o=\frac{32}{16} \\ y_o=2 \end{gathered}$

The initial number of lions in the park is 2

(b)

Since we have the initial amount and the common ratio, the equation is given by:

$y=2\cdot(4)^x$