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)^{(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)^{(t)/(2)} \\ 130=16(2)^{(t)/(2)} \\ (130)/(16)=\frac{16(2)^{(t)/(2)}}{16} \\ (130)/(16)=(2)^{(t)/(2)} \end{gathered}`

Then,

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

Then,

`\begin{gathered} t\ln (2)=2ln((65)/(8)) \\ t=(2ln((65)/(8)))/(\ln (2)) \\ t=6.044 \end{gathered}`

Hence, the value of years is 6.