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

d. 194481

Step-by-step 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

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.