Answer:
6% of 50 is 3 flies per day
50/3 is 16 days
i'd say the answer is A) 18 days
The number of days that are needed to double the population of the fruit flies from 50 is 12 days.
Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time. It is given by the formula,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where, A is the value after t period of time, and,
r is the rate of interest.
As it is given that the population of the fruit flies at the beginning is 50, while the rate at which the population is increasing is 6% per day, therefore, the population of the fruit flies will increase by 6% every day. Thus, the population will compound at a rate of 6% per day.
We know that formula of the compounding is written as,
[tex]A = P(1+\dfrac{r}{100})^n[/tex]
A is the Final quantity,
P is the Initial quantity,
r is the rate, and n is the time period.
We know that initially there were 50 fruit flies, and we need to calculate the time in which the population will be doubled, therefore, the population will be 100. Substitute the value to find the time period,
[tex]A = P(1+\dfrac{r}{100})^n\\\\100 = 50(1+\dfrac{6}{100})^n\\\\100=50(1.06)^n\\\\2 = 1.06^n[/tex]
Taking the logs,
[tex]\rm n= log_{1.06}2\\\\n = 11.89 \approx 12[/tex]
hence, the number of days that are needed to double the population of the fruit flies from 50 is 12 days.
Learn more about Compound:
https://brainly.com/question/25857212
