Answer: y=C(1+r)t
Step-by-step explanation:
The general exponential growth model is y=C(1+r)t , where C is the initial amount or number, r is the growth rate (for example, a 2% growth rate means r=0.02 ), and t is the time elapsed.
Example 1:
A population of 32,000 with a 5% annual growth rate would be modeled by the equation:
y=32000(1.05)t
with t in years.
Sometimes, you may be given a doubling or tripling rate rather than a growth rate in percent. For example, if you are told that the number of cells in a bacterial culture doubles every hour, then the equation to model the situation would be: y=C⋅2t (with t in hours).
Example 2:
Suppose a culture of 100 bacteria is put into a petri dish and the culture doubles in size every hour. Predict the number of bacteria that will be in the dish after 12 hours.
P(t)=100⋅2t
P(12)=100⋅212=409,600 bacteria