If a child is 32 inches tall at 3 years and 39 inches tall a

If a child is 32 inches tall at 3 years and 39 inches tall at 6 years and we assume that her growth is linear, find an equation representing her height as a function of her age and use it to find out how tall she will be when she is 15.

Solution

Child is 32 inches at 3yrs

Child is 39 inches at 6 years

Linear equation: Find the equation of line passing through ( age, height) --->(x , y) ---( 3, 32) and ( 6, 39)

slope =( 39 -32)/( 6-3) = 7/3

Slope Intercept form : y = mx+c ---> y = 7x/3 +c

32= 3*(7/3) +c ----> c= 32 -7 = 25

So, y = 7x/3 +25

Let y= h(x) .So, we can write : h(x) = 7x/3 +25

whe she is 15yrs old ; x = 15 yrs

h(x) = 7*15/3 + 25 = 37 +25 = 62 inches