Question

A farmer increased his yield by 5% each year over the last five years. If he produced 600 tonnes this year, calculate to the nearest tonne his yield five years ago.​

Answer 1

$\sf\small\green{Given:-}$

• Increase yield= 5%

• produced = 600 tones.

$\sf\small\green{Find:-}$

• calculate to the nearest tonne his yield five years ago.

$\sf\small\green{Solution:-}$

$\rightarrow\sf \: x(1 + \dfrac{5}{100} ) ^{5} = 600$

$\rightarrow \sf \: x( \dfrac{105}{100} ) ^{5}$

$\rightarrow \sf \: x = 600 \times ( \frac{100}{1.5} ) ^{5}$

$\rightarrow\sf \: x = \dfrac{600 \times 100 \times 100 \times 100 \times 100 \times 100}{105 \times 105 \times 105 \times 105 \times 105}$

$\rightarrow\sf \: x= \dfrac{600 \times 20 \times 20 \times 20 \times 20 \times 20}{21 \times 21 \times 21 \times 21 \times 21}$

$\rightarrow\sf \: x = \dfrac{600000 \times 3200000}{441 \times 441 \times 21}$

$\rightarrow \sf \: x = 470115.699$

$\sf \dashrightarrow\fbox \red{x = 470.116 \: tone}$

#Quality answer.