Question

A shepherd has 200 sheep with him. Find the number of sheeps with him after 3 years if the increase in number of sheeps is 8% every year.

Answer 1

Hi ,

Number of sheep in the bigginng = 200

increasing percent each year ( g ) = 8%

Number of sheep after 3 years =

200[(100 + g )/100 ]³


= 200[( 100 + 8 )/100 ]³

= 200 × ( 108/100 )³

= 251.94

≈ 251

I hope this helps you.

: )

Answer 2

Answer:

The number of sheep after 3 years is 251.

Step-by-step explanation:

The exponential increase function is given by

$y = a (1 + r)^{t}$

Where a is the initial value, r is the rate of interest in the decimal form and t is the time.

As given

A shepherd has 200 sheep with him.

if the increase in number of sheeps is 8% every year.

a = 200

8% is written in the decimal form.

$= \frac{8}{100}$

= 0.08

t = 3 years

Put all the value in the exponential increase function.

$y = 200(1 +0.08)^{3}$

$y = 200(1.08)^{3}$

$y = 200\times 1.2597$

y = 251.94

y = 251 (Approx)

Therefore the number of sheep after 3 years is 251.