Question

the table shows the balance of the money market account overtime write a function that represents the balance Y in dollars after T years

Answer 1

Let's begin by identifying key information given to us:

`(t,b)=(0,500),(1,475),(2,451.25),(3,428.69),(4,407.25),(5,386.89)`

We will proceed to calculate for the slope of this function. We have:

`\begin{gathered} m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ m=(475-500)/(1-0)=(451.25-475)/(2-1)\Rightarrow(-25)/(1)=(-23.75)/(1) \\ m=-25\\e-23.75 \\ \therefore This\text{ is not a linear function} \\ \end{gathered}`

We will proceed to find the common ratios as shown below:

`\begin{gathered} r=(475)/(500)=(451.25)/(475)\Rightarrow(95)/(100)=(95)/(100)=0.95 \\ r=\text{0}.95 \\ \therefore\text{This is an exponential function} \\ \\ \end{gathered}`

This exponential equation is given by: