Answer:
- t = 0: 372
- t = 4 hours: 24,382,480
Explanation:
You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.
Equation
We like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...
(minutes, population) = (110, 60000)
We can put these numbers in the form ...
p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))
where the growth factor (2) is applicable over the growth period (15 minutes).
This makes our equation ...
p(t) = 60000(2^((t-110)/15))
Values
We want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.
The population at t=0 was about 372.
The population after 4 hours will be 24,382,480.
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Additional comment
A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...
p(t) = 372·e^(0.0452098t)
where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15
These rounded numbers don't give the problem statement values exactly:
p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).
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