A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies and predicts the stock will grow by 38% each day. Which function could she use to calculate , the number of days required for her stock to grow to n fruit flies

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10-06-2022
Biology

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A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies and predicts the stock will grow by 38% each day. Which function could she use to calculate , the number of days required for her stock to grow to n fruit flies

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shristiparmar1221 shristiparmar1221 · Answer 1 · 2022-06-21T17:10:57+02:00

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)

What is Compounding growth ?

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:

brainly.com/question/24924853

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okpalawalter8 okpalawalter8 · Answer 2 · 2022-06-21T17:52:17+02:00

A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies, The function she could use to calculate is mathematically given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)