SOLUTION: A new virus increases exponentially at the monthly rate of 2.8%. Four months after the initial outbreak, there were 10,000 reported cases. (Exponential Growth) a. How many were

Question 1175529: A new virus increases exponentially at the monthly rate of 2.8%. Four months
after the initial outbreak, there were 10,000 reported cases. (Exponential
Growth)
a. How many were initially infected with the virus?
b. Model the number of reported case as a function of time.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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:

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.
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