Respuesta :
A. Every month Population will increase by a factor of 0.84%.
B. Every 3 months Population will increase by a factor of 2.5%.
C. Increase in population in every 20 months is 10% + 6.72% = 16.72%.
Step-by-step explanation:
Here, we have number of employees in a company has been growing exponentially by 10% each year. So , If we have population as x in year 2019 , an increase of 10% in population in 2020 as [tex]x + \frac{x}{100}\times10[/tex] which is equivalent to [tex]\frac{11x}{10}[/tex].
A.
For each month: We have 12 months in a year and so, distributing 10% in 12 months would be like [tex]\frac{10}{12} = 0.84[/tex] . ∴ Every month Population will increase by a factor of 0.84%.
B.
In every 3 months: We have , 12 months in a year , in order to check for every 3 months [tex]\frac{12}{3} = 4[/tex] and Now, Population increase in every 3 months is [tex]\frac{10}{4} = 2.5[/tex]. ∴ Every 3 months Population will increase by a factor of 2.5%.
C.
In every 20 months: We have , 12 months in a year in which increase in population is 10% . Left number of moths for which we have to calculate factor of increase in population is 20-12 = 8. For 1 month , there is 0.84% increase in population ∴ For 8 months , 8 × 0.84 = 6.72 %.
So , increase in population in every 20 months is 10% + 6.72% = 16.72%.
Answer:
a. Each month = 1.00797414043
b. Every 3 months = 1.02411368909
c. Every 20 months = 1.17216246047
Given that the number of employees in a company has been growing exponentially by 10% each year. So the growth factor per year is = (1 + 10%) = 1 + 0.10 = 1.10.
1 year = 12 months.
That means the monthly growth factor is: [tex]1.10^{\frac{1}{12}}=1.00797414043[/tex].
The growth factor every 3 months is = [tex]\left(1.10^{\frac{1}{12}}\right)^{3}=\left(1.00797414043\right)^{3}=1.02411368909[/tex]
The growth factor every 20 months is =
[tex]\left(1.10^{\frac{1}{12}}\right)^{20}=\left(1.00797414043\right)^{20}=1.17216246047[/tex].
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