Question

T(t)=5^T using this model when it will take to reach approximately 300 female turtle? how many female turtle will there be in 7 years?

Answer 1

0. 3.5 years (approximately)

,

1. 78,125 female turtles.

1) SInce the equation that models this situation, the population of female turtles is:

$T(t)=5^t$

2) Then we can calculate that population in 7 years, by plugging t =7 and considering that the initial value is 5 then we can write when there will be 300 turtles:

$\begin{gathered} T(t)=5^t \\ 300=5^t \\ \log _{10}300=\log _{10}5^t \\ 2.477=t\log _{10}5 \\ 0.96897t=2.477121 \\ \frac{0.96897t}{0.96897}=\frac{2.477121}{0.96897} \\ t=3.54\text{ }\approx3.5\text{ years} \end{gathered}$

• Note that we had to use the properties of a logarithm to find that out.

,

• Rounding off to the nearest tenth, then approximately within 3.5 years there will be 300 turtles up there.

b) To find out how many female turtles will there be in 7 years? ​

We'll plug into that function t =7

$\begin{gathered} T(7)=5^7 \\ T(7)\text{ = 78,125} \end{gathered}$

Hence, we'll have 78, 125 female turtles.