Question 1176097
the bank is offering 5% compounded quarterly.
you deposit 20,000 now.
your exponential formula is y = a * b^x
a = 20,000
b = .10/4 = .025 + 1 = 1.025
formula becomes y = 20,000 * 1.025 ^ x
this formula can be graphed as shown below:


<img src = "http://theo.x10hosting.com/2021/030103.jpg"


you can see that the formula is exponential from the long term view shown below.


<img src = "http://theo.x10hosting.com/2021/030104.jpg"


if  you let y = f and a = p and b = (1 + r) and x = n, then you get the formula:


f = p * (1 + r) ^ n


f is the future vlaue
p is the present value
r is the interest rate per time period
n is the number of time periods.


when p = 20,000 and r = 10% per year, the formula becomes:


f = 20,000 * (1 + .10/4) ^ n


.10/4 is the interest rate per quarter.
n is the number of quarters.


simplify this formula to get:


f = 20,000 * 1.025 ^ n


that's the same exponential formula as y = 20,000 * 1.025 ^ x, where a = 20,000 and b = 1.025