SOLUTION: The relative growth rate for a certain type of bacteria population is 78% per hour. A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the cult

Question 1071198: The relative growth rate for a certain type of bacteria population is 78% per hour. A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture. What is the initial number of bacteria in the culture?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
discrete compound growth rate formula is:

f = p * (1+r)^n

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

the growth rate is 78% per hour = .78
the time period is hours.

in 5 hours, there are 34,820 bacteria in the culture.

formula becomes

34820 = p * 1.78^5

divide both sides of this equation by 1.78^5 and solve for p to get:

p = 34820 / 1.78^5 = 1948.627177

in 5 hours, 1948.627177 bacteria will have grown to be equal to 1948.627177 * 1.78^5 = 34820 bacteria.

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