Question

Choose the correct option. (0.5 Marks)
The number of feral cats in a wildlife reserve increases by 15% each year. If there were originally 200
feral cats in the reserve, the recurrence relation for the number of feral cats Cn after n years is:​

Answer 1

SOLUTION

GIVEN

The number of feral cats in a wildlife reserve increases by 15% each year. If there were originally 200 feral cats in the reserve

TO DETERMINE

The recurrence relation for the number of feral cats $\sf{C_n}$ after n years

CONCEPT TO BE IMPLEMENTED

If initially the number of items = P and it increases at r % per year then the number of items after n years

$\displaystyle \sf{C_n = P { \bigg(1 + \frac{r}{100} \bigg)}^{n} }$

EVALUATION

Here originally 200 feral cats in the reserve

So P = 200

Rate of increment per year = r % = 15 %

The recurrence relation for the number of feral cats $\sf{C_n}$ after n years

$\displaystyle \sf{C_n = P { \bigg(1 + \frac{r}{100} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \: C_n = 200 \times { \bigg(1 + \frac{15}{100} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \: C_n = 200 \times { \bigg(1 + \frac{3}{20} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \: C_n = 200 \times { \bigg(\frac{23}{20} \bigg)}^{n} }$

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