Question

I really need help with this question!! How do you solve it?In 1985, they discovered a new sea creature. It was found to have an initial population of 832. Assuming the population was growing at a rate of 2.3% each year, when will the population exceed 1500?

Answer 1

The growth rate is given below as

`r=2.3\%`

The initial population is

`P_0=832`

The exponential growth formula is given below as

`\begin{gathered} P=P_0(1+r)^t \\ 832(1+(2.3)/(100))^t=1500 \\ 832(1.023)^t=1500 \\ (1.023)^t=(1500)/(832) \\ (1.023)^t=1.803 \\ take\text{ ln of both sides} \\ ln(1.023)^t=ln(1.803) \\ tln(1.023)=ln(1.803) \\ t=(ln(1.803))/(ln(1.023)) \\ t=25.9years \\ \end{gathered}`

Hence,

The final answer is

The population will exceed 1500 in approximately 26 years' time