Question 1175529
the formula you can use is:


f = p * (1 + r) ^ n


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


in your problem:


f is equal to 10,000
r is equal to .028 per month
n is equal to 4 months.


the formula becomes:


10,000 = p * (1 + .028) ^ 4


solve for p to get:


p = 10,000 / (1 + .028) ^ 4 = 8954.215481.


confirm by replacing p in the original equatio n and solving for f.


equation becomes f = 8954.215481 * (1 + .028) ^ 4


solve for f to get:


f = 10,000.


this confirms the value of p is good.


the reported cases as a function of time is f = 8954.215481 * 1.28 ^ n


f is the future vlue.
p is the present value which is equal to 8954.215481.
r is equal to .028 per month.
n is the number of months.


this equation can be graphed by replacing f with y and n with x.
the graph is shown below:


<img src = "http://theo.x10hosting.com/2021/022101.jpg" >


you can see that when x = 4, y = 10,000.


the growth is exponential.


when x = 36, y = 1.028^36 = 24198.01096 which is equal to 24198.011 when rounded to 3 decimal places, as shown on the graph.


the formula is exponential because it is of the form of y = a * b ^ x, with a = 8954.215481 and b = 1.028 and x = the exponent.