The number of bacteria in a petri dish on the first day was 252252 cells. If the number of bacteria increase at a rate of 57%57% per day, how many bacteria cells will there be after 77 days?
Question
The number of bacteria in a petri dish on the first day was 252252 cells. If the number of bacteria increase at a rate of 57%57% per day, how many bacteria cells will there be after 77 days?
Solution
To solve this problem, we need to use the formula for compound interest, which is also applicable to population growth problems. The formula is:
A = P(1 + r/n)^(nt)
where:
- A is the amount of money (or in this case, bacteria) that will be in the account (or petri dish) after t years (or days),
- P is the principal amount (the initial amount of money, or bacteria),
- r is the annual interest rate (or daily growth rate),
- n is the number of times that interest is compounded per unit t,
- t is the time the money is invested or borrowed for, in years (or the number of days the bacteria are growing).
In this case, the initial number of bacteria (P) is 252252, the daily growth rate (r) is 57% or 0.57 (in decimal form), and the number of days (t) is 77. Since the bacteria are growing continuously over the day, we can consider n as 1.
Substituting these values into the formula, we get:
A = 252252(1 + 0.57/1)^(1*77)
Solving this equation will give us the number of bacteria in the petri dish after 77 days.
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