parametric equations

Question

A farmer recently planted a new crop of cherry trees in his orchard. The first year the trees grow to 10 feet  tall and produuce 3 1/2 pounds of cherries each. THe trees grow at the rate of 1 1/2 feet per year and increase their production of cherries by 3/4 pounds each year.

a. write a system of parametric equations to determine the height h(t) of a tree in t years and its cherry production c(t) in  t years.

b express the cherry production, c, as a dunction of height, h.

Answer 1

Let time t be measured in years then,

1) h(t) = 10 + 1.5t

and

c(t) = 3.5 + 0.75t   ----------(1)

2) h(t) = 10 + 1.5t

or t = {h(t) - 10}/1.5

On putting the value of t in (1) we get:

c(t) = 3.5 + 0.75{h(t) -10}/1.5

or c(t) = 0.5h(t) - 1.5