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Question
A shepherd has 200 sheep with him. Find the number of sheep with him after 3 years if the increase in the number of sheep is 8% every year.
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Solution
Here, P = Number of sheep initially = 200
A = Number of sheep after 3 years
R = Rate of increase in the number of sheep per year = 8%
N = 3 years
A = P `(1 + "R"/100)^"N"`
= 200 `(1 + 8/100)^3`
= `200((100 + 8)/100)^3`
= `200(108/100)^3`
= `200((27 xx 4)/(25 xx 4))^3`
= `200(27/25)^3`
= `200 xx 27/25 xx 27/25 xx 27/25`
= `8 xx 27 xx 27/25 xx 27/25`
= `0.32/25 xx 27 xx 27 xx 27`
= `0.0128 xx 27 xx 27 xx 27`
= 251.9424
= 252
∴ The number of sheep with the shepherd after 3 years would be 252 (approx).
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