Question

Six guinea pigs are released in an area with no natural predators. The guinea pig population quadruples every year. Write a function p that represents the guinea pig population at a given time t measured in years

Answer 1

SOLUTION:

Case: Exponential equation

Method:

Initial population: 6

Quadruple each year, multiplier= 4.

Where t is the number of years, the population is:

$P=6(4)^t$

a) The inverse is calculated as:

$\begin{gathered} \frac{P}{6}=4^t \\ log(\frac{P}{6})=log4^t \\ log(\frac{P}{6})=tlog4^ \\ t=\frac{log(\frac{P}{6})}{log(4)} \\ P^{-1}=\frac{log(\frac{t}{6})}{log(4)} \end{gathered}$

b) Approximately how long to reach 1000 guinea pigs

$\begin{gathered} P^{-1}=\frac{log(\frac{1000}{6})}{log(4)} \\ P^{-1}=3.69 \end{gathered}$

Final answers:

a)

$P^{-1}=\frac{log(\frac{t}{6})}{log(4)}$

b)

$P^{-1}\approx3.7$