Question

Hello. Need to solve problem four. I’m addition need to estimate the length at three year old Gila and Estimate the age of a 25 cm long GilaThank you

Answer 1

Since the lizard increases by about 8% each year, it can be understood as an exponential function as:

$L(t)=L_0\ast(1+r)^t$

since the initial length and the rate of increase is also given, replace ins the formula

$\begin{gathered} L(t)=16\ast(1+0.08)^t \\ simplify \\ L(t)=16\ast(1.08)^t \end{gathered}$

Then replace in the formula t as 3

$\begin{gathered} L(3)=16\ast(1.08)^3 \\ L(3)=20.155\cong20.16cm \end{gathered}$

Answer:

The equation that models the length of the lizard for the first 8 years is:

$L(t)=16(1.08)^t$

And the approximate length of the lizard after 3 years is about 20.16 cm