Answer and Step-by-step explanation: The graph is shown in the attachment.
a. ΔR on [1,2] is mathematically expressed as:
ΔR = R(2) - R(1)
which means difference of population of rabbits after 2 months and after 1 month.
[tex]R(1) = 100(\frac{2}{5}.1 )[/tex]
[tex]R(1) = 100(\frac{2}{5} )[/tex]
R(2) = [tex]100(\frac{2}{5}.2 )[/tex]
[tex]R(2) = 100(\frac{4}{5} )[/tex]
[tex]\Delta R = 100(\frac{4}{5} )-100(\frac{2}{5} )[/tex]
[tex]\Delta R = 100[\frac{4}{5} - \frac{2}{5} ][/tex]
[tex]\Delta R=[/tex] 40
Difference of rabbits between first and second months is 40.
b. R(0) = 100([tex]\frac{2}{5} .0[/tex])
R(0) = 0
Initially, there no rabbits in the population.
c. R(10) = [tex]100(\frac{2}{5}.10 )[/tex]
R(10) = 400
In 10 months, there will be 400 rabbits.
d. R(t) = 500
[tex]500=100(\frac{2}{5}.t )[/tex]
[tex]\frac{500}{100}=\frac{2}{5}.t[/tex]
[tex]t = \frac{500.5}{100.2}[/tex]
t = 12.5
In 12 and half months, population of rabbits will be 500.
