Question

An iguana is about 42 cm. at birth and increases in length at an approximate rate of 12% per week. Write the function which models the growth. Use X for the number of weeks and y for the length of the iguana.

Answer 1

We were given that:

The iguana is 42cm at birth

It increases by 12% every week; r = 12% = 0.12

The number of weeks is represented by ''x'' & the length of the Iguana is represented by ''y''

This function is represented by the expression below:

`\begin{gathered} f\mleft(x\mright)=a\mleft(1+r\mright)^x \\ where\colon r=growth.rate \\ a=initial.length \\ f\mleft(x\mright)=y \\ \Rightarrow y=a(1+r)^x \\ y=a(1+r)^x \\ a=42,r=0.12 \\ \text{Substituting the variables into the equation, we have:} \\ y=42(1+0.12)^x \\ y=42(1.12)^x \\ \\ \therefore y=42(1.12)^x \end{gathered}`