Question

How many years does it take for 130 acres of wetland to be infested

Answer 1

As given by the question

There are given that the equation

$u(t)=16(2)^{\frac{t}{2}}$

Now,

Put the value 130 into the given equation instead of u(t) and find the value of t

Then,

$\begin{gathered} u(t)=16(2)^{\frac{t}{2}} \\ 130=16(2)^{\frac{t}{2}} \\ \frac{130}{16}=\frac{16(2)^{\frac{t}{2}}}{16} \\ \frac{130}{16}=(2)^{\frac{t}{2}} \end{gathered}$

Then,

$\begin{gathered} \frac{130}{16}=(2)^{\frac{t}{2}} \\ \frac{t}{2}\ln (2)=ln(\frac{130}{16}) \\ \frac{t}{2}\ln (2)=ln(\frac{65}{8}) \end{gathered}$

Then,

$\begin{gathered} t\ln (2)=2ln(\frac{65}{8}) \\ t=\frac{2ln(\frac{65}{8})}{\ln (2)} \\ t=6.044 \end{gathered}$

Hence, the value of years is 6.