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unknown6669

04.12.2022

Mathematics

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.

$R(1) = 100(\frac{2}{5}.1 )$

$R(1) = 100(\frac{2}{5} )$

R(2) = $100(\frac{2}{5}.2 )$

$R(2) = 100(\frac{4}{5} )$

$\Delta R = 100(\frac{4}{5} )-100(\frac{2}{5} )$

$\Delta R = 100[\frac{4}{5} - \frac{2}{5} ]$

$\Delta R=$ 40

Difference of rabbits between first and second months is 40.

b. R(0) = 100( $\frac{2}{5} .0$ )

R(0) = 0

Initially, there no rabbits in the population.

c. R(10) = $100(\frac{2}{5}.10 )$

R(10) = 400

In 10 months, there will be 400 rabbits.

d. R(t) = 500

$500=100(\frac{2}{5}.t )$

$\frac{500}{100}=\frac{2}{5}.t$

$t = \frac{500.5}{100.2}$

t = 12.5

In 12 and half months, population of rabbits will be 500.

A population of rabbits is described by the function R(t) = 100(2t/5), where t is measured in months

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