Question

I am unsure how to solve this ,this is a practice sheet

Answer 1

The model function is

`P(t)=12*3^(0.498t)`

where t is the time in days and P(t) is the population along the time.

Question a.

Initially, at t=0, the population is

`\begin{gathered} P(0)=12*3^0 \\ P(0)=12*1 \\ P(0)=12 \end{gathered}`

that is, there was 12 fruits.

Question b.

After t=6, we have

`\begin{gathered} P(6)=12*3^(0.498\cdot6) \\ P(6)=12*3^(2.988) \\ P(6)=12*26.646 \\ P(6)=319.76 \end{gathered}`

that is, by rounding up, there will be 320 fruits.

Question c.

In this case, we have P(t)=8 000, then we have

`8000=12*3^(0.498t)`

If we move 12 to the left hand side, we get

`\begin{gathered} (8000)/(12)=3^(0.498t) \\ 666.666=3^(0.498t) \end{gathered}`

By applying natural logarithms on both sides, we obtain

`\log 666.666=0.498t\log 3`

then, t is equal to

`t=\frac{\log \text{ 666.666}}{\text{0.498log3}}`

therefore, t is

`\begin{gathered} t=(6.502)/(0.498(1.098)) \\ t=(6.502)/(0.547) \end{gathered}`

and t is equal to 11.88 days. By rounding up, t=12 days.

Question d.

The number of fruits