Question

Smith has a dairy farm in which the number of cows increases at the rate of 5% per annum which results in the increase in the production level of the milk by 10% per annum. But the demand of the milk is increasing at the rate of the population of the town. If initially the farm has 160000 cows then the number of cows needed after 4 years to fulfill the requirement of the milk is: a. 204481 b.214481 c. 194440 d.194481 e. None of these

Answer 1

d. 194481

Explanation:

We solve this question using exponential growth rate formula

This is given as:

y = a(1 + r) ^t

Where y = Amount after time t

a = Initial amount = 160000

r = growth or increase rate = 5% = 0.05

t = time in years = 4

y = 160000(1 + 0.05)⁴

y = 160000(1.05)⁴

y = 194481

Therefore, the number of cows needed after 4 years to fulfill the requirement of the milk is 194481