Answer:
4.16% is the hourly growth rate
Step-by-step explanation:
What we can do here is to first set up an exponential relationship that relates the present number of bacteria, the initial number of bacteria, the growth rate of the bacteria and the number of hours.
What we want to establish here has a resemblance with the compound interest formula in finance.
Let’s see the initial number of bacteria as the amount deposited, the present number of bacteria as the amount after some months, the growth rate as the monthly percentage while the number of hours works like the number of months.
Mathematically, what we have will be;
P = I(1 + r)^h
where P is the present bacteria number, I is the initial, r is the growth rate while h is the number of hours.
Thus, we have the following values from the question;
P = 1530
I = 1,300
r = ?
h = 4
Substituting these values, we have;
1530 = 1300(1 + r)^4
divide both sides by 1,300
1.177 = (1+r)^4
Find the fourth root of both sides
(1.177)^(1/4) = 1+ r
1.0416 = 1 + r
r = 1.0416-1
r = 0.0416
This in percentage is 4.16%
