5.a).
GIven:
Principal P= $ 5000.
Interest rate R = 7 % =0.07.
The number of years T=x.
Consider the following formula to find the amount.
[tex]A=P(1+r)^t[/tex]
Substitute A=y P=5000, R=0.07, and T=x in the equation, we get
[tex]y=5000(1+0.07)^x[/tex]
[tex]y=5000(1.07)^x[/tex]
Which is of the form
[tex]y=a(b)^x[/tex]
We know that this is the exponential growth function.
Hence the exponential function is
[tex]y=5000(1.07)^x[/tex]
b)
Consider the y values from the table.
5,10,15,20,25,30,...
The difference between 5 and 10 = 10-5 =5.
The difference between 10 and 15 = 15-10 =5.
Proceed this way to find the common difference.
The common difference is 5.
The y value is increasing by the common value of 5.
The slope =5 and the y-intercept is 5 from point (0,5).
The equation is
[tex]y=5+5x[/tex]
This is a linear equation.
