Question

. A species of frog’s population grows 24% every year. Suppose 100 frogs are released into a pond.How many years will it take for there to be at least 1000 frogs?

Answer 1

ANSWER

It will take 10.71 years for the frogs to grow from 100 to 1000

Explanation:

Given information

The initial population of the frogs = 100

Percentage increase = 24%

The final population of the growth = 1000 frogs

time =?

Step 1: Write the general formula for calculating the size of a population

`P=P_O(1+r)^t`

Where

P = Final population

Po = initial population

r = rate

t = time

Step 2= convert the growth rate from percentage to decimal

`\begin{gathered} r\text{ = 24 \%} \\ r\text{ = }(24)/(100) \\ r\text{ = 0.24} \end{gathered}`

Step 3: Substitute the given data into the above formula and solve for t

`\begin{gathered} 1000=100(1+0.24)^t \\ \text{Divide both sides by 100} \\ (1000)/(100)\text{ = }(100)/(100)(1+0.24)^t \\ 10=(1+0.24)^t \\ 10=(^{}1.24)^t \\ \text{Take the logarithms of both sides} \\ \text{log 10 = t log(1.24)} \\ 1\text{ = t }*\text{ 0.0934} \\ 1\text{ = 0.0934t} \\ \text{Divide both sides by 0.0934} \\ (1)/(0.0934)\text{ = }\frac{\cancel{0.0934}t}{\cancel{0.0934}} \\ t\text{ = 10.71 years} \end{gathered}`

Hence, it will take 10.71 years for the frogs to grow from 100 to 1000