Question

A frog starts 24 feet from a wall and gets halfway to the wall on each jump.

Answer 1

First let us graph the function

`y=24(0.5)^x`

The graph is shown below

(b) After 4 jumps how far will the frog be from the wall

We will substitute x = 4 into the equation, we have

`\begin{gathered} y=24(0.5)^x \\ y=24(0.5)^4 \\ y=24*0.0625 \\ y=1.5 \end{gathered}`

Hence the answer is 1.5 feet

(c) Since the tongue of the frog is 1 inch. And the model was given in feet, we will convert 24 feet to inches, we have

`\begin{gathered} 1feet=12inches\text{ } \\ 24feets=24*12 \\ =288\text{ inches } \end{gathered}`

So if the from tongue can reach 1 in. from the wall, we put y = 1 and find x with the new model for inches as

`\begin{gathered} y=288(0.5)^x \\ 1=288(0.5)^x \\ 0.5^x=(1)/(288) \\ taking\text{ logs} \\ log0.5^x=log((1)/(288)) \\ xlog0.5=log((1)/(288)) \\ x=(log((1)/(288)))/(log0.5) \\ x=8.16999 \end{gathered}`

Hence the answer is approximately 8 jumps