Question

Suppose 12 hamsters were studied in a lab. The population of the hamstersquadruples every 3 years. How many hamsters will there be in 15 years?What is the equation of the function?

Answer 1

The exponential growth can be expressed as

$y=y_0e^{kt}$

y0 is the initial value

k is the growth rate

t is the time period

y is the final value

If you write the final value of the population as a function of the time, for k=4 and y0=12 the formula is

$y=12e^{4t}$

t is the determined time period the population grows, if it cuadruples every 3 years, then

first 3 years is t=1

6 years is t=2

9 years is t=3

12 years is t=4

15 years is t=5

For this population

$\begin{gathered} y=12e^{4\cdot5} \\ y=12e^{20} \\ y=5,821,982,345 \end{gathered}$