Question

Ever since renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t)h(t)h, left parenthesis, t, right parenthesis models the height of the tree (in centimeters), ttt years since renata moved in. h(t)=210+33th(t)=210+33th, left parenthesis, t, right parenthesis, equals, 210, plus, 33, t how tall was the tree when renata moved in?

Answer 1

It was 210 cm.

The function she used is h(t) = 210 + 33t.  This is a linear function, since it is of the form f(x) = mx+b.  In a linear function, we have the slope, m, which tells us how much the height increases per year, and the y-intercept, b, which tells us how tall it was when we began measuring.  Our m value would be 33 and our b would be 210, so the original height was 210.

Answer 2

Answer:

The height of tree when renata moved in, is 210 cm.

Step-by-step explanation:

The given function is

$h(t)=210+33t$

where, h(t) is height of the tree outside her window after t years since renata moved in.

The initial height of tree is h(0). It means the value of function at t=0 represents the height of tree when renata moved in.

Substitute t=0 in the given function.

$h(0)=210+33(0)$

$h(0)=210+0$

$h(0)=210$

Therefore, the height of tree when renata moved in, is 210 cm.