Question

Fruit Company A recently released a new applesauce. By the end of its first year, profits on this product amounted to $37,100. The anticipated profit for the end of the fourth year is$58,400. After the first year, the ratio of change in time to change in profit is constant. Let x be years and P be profit.a. Write a linear function P(x) that expresses profit as a function of time.c. Predict when the profit should reach $108,100.The profit should reach $108,100 in years

Answer 1

Answer: 11 year

P(1) = 37,100

P(4) = 58,400

The linear equation (for x ≥ 1)

P(x) = 37,100 + a(x-1)

For x = 4

58,400 = 37,100 + a(4-1)

58,400 - 37,100 = 3a

21300 = 3a

a = 7100

So, the linear equation:

P(x) = 37100 + 7100*(x-1)

P(x) = 37100 + 7100x - 7,100

P(x) = 7100x + 30000

To find when the profit should reach 108100, we can substitute P(x) by 108100.

108100 = 7100x + 30000

108100 - 30000 = 7100x

78100 = 7100x

x = 78100/7100

x = 11

Answer: 11 year