Respuesta :
Step 1: Write out the formula
[tex]\begin{gathered} f(t)=a(1+r)^t \\ \text{where} \\ f(x)=\text{ area occupied by the cane toad} \\ a=\text{ initial amount} \\ r=\text{ growth rate} \\ t=\text{ number of years} \end{gathered}[/tex]Step 2: Substitute the given values
From the table, we can see that
[tex]f(0)=a=36500\operatorname{km}^2[/tex][tex]\begin{gathered} f(5)=a(1+r)^5=53600 \\ \text{ This implies that} \\ 36500(1+r)^5=53600 \\ \text{thus} \\ (1+r)^5=\frac{53600}{36500} \\ \text{Therefore} \\ (1+r)^5=\frac{536}{365} \\ \text{thus} \\ 1+r=\sqrt[5]{\frac{536}{365}}\approx1.0799 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence,} \\ r=1.0799-1=0.0799 \end{gathered}[/tex]Therefore,
[tex]f(t)=36500(1.0799)^t[/tex]Step 3: Substitute time t = 40 into f(t)
[tex]f(40)=36500(1.0799)^{40}=790013\approx800000[/tex]Therefore, based on the data, the measurement that is closest to the number of square kilometers of land that will be occupied by cane toads 40 years after this is 800000
