The given question belongs to the concept of compounding growth.
The function could she use to calculate, the number of days required for her stock to grow to n fruit flies will be log₁.₃₈ (n/100)
<h3>What is Compounding growth ?</h3>
Compound growth as the average rate of growth experienced by an investment over a multi-year period.
Compound annual growth rate, or CAGR, is the mean annual growth rate of an investment over a specified period of time longer than one year
The steps to solve this problem are as follow :
The geneticist currently has a stock of 200 fruit flies and predicts the stock will grow by 38% each day
let f(n) denote number of days required for her stock to grow to 'n' fruit flies
Now, the growth here represents a compounded growth with a growth rate of 38% each day
Using following formula for compound growth :
A = p(1+r/100)ⁿˣ
Where,
A = number of fruit flies
P = initial number of fruit flies = 200
r = rate of growth = 38%
n = number of times compounded per time period = 1 per day
x = time period = f(n) days
A = 200(1+38/100)^f(n)
n/200 = (1.38)^f(n)
Applying log both side whose base is 1.38 we get,
f(n) = log₁.₃₈ (n/100)
So,the function could she use to calculate, the number of days required for her stock to grow to n fruit flies will be log₁.₃₈ (n/100)
Learn more about Compounding growth here:
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