Charlotte planted her tomato plant it grew 3 inches in 1week. After 5weeks, the tomato plant was 23 inches tall the relationship is linear interpret the rate of

Question

When Charlotte planted her tomato plant, it grew 3 inches in one week. After 5 weeks, the tomato plant was 23 inches tall. Assume the relationship is linear. Find and interpret the rate of change and the initial value.

Answer 1

The growth rate is r = 3 inches/week. A linear growth rate means that the slope of the height vs time graph is a constant, which we have said is r.

 

We don't know the initial height of the plant. So after 5 weeks, we have:

 

(23 - x) /5 = r

 

23 -x = 5 * r = 5 * 3 = 15

 

So

 

x = 8 inches.

 

The linear relation is:

 

h = r * t + h0

where

h0 = 8 inches, at t0 = 0 (initial condition, where all times in this problem are relative to t0. Setting t0 = 0

makes the math simpler. We could have written h = r * (t - t0) + h0. Note that r = (h-h0)/(t-t0) = (23 - 8)/5 = 3.)

 

h = 3 * t + 8

 

Check:

 

h = 3 * 5 + 8 = 23  (check!)