Corrected Question
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in.
H(t)=210+33t
(a)How tall was the tree when Renata moved in?
(b)How fast does the tree grow?
Answer:
(a)210cm
(b)33cm per year
Step-by-step explanation:
(a)Given the height function of the tree, H(t) where t is the number of years since Renata moved in.
When she moved in, the number of years, t=0
Therefore, we substitute t=0 in H(t) to find the height of the tree when she moved in.
[tex]H(t)=210+33t\\H(0)=210+33(0)\\H(0)=210cm[/tex]
The height of the tree when she moved in was 210cm.
(b)
To determine the rate at which the tree grows, we can find the derivative of the height function.
Given the height function, [tex]H(t)=210+33t[/tex]
[tex]\dfrac{dH}{dt}=33[/tex]
Therefore, we conclude that the tree grows at a rate of 33cm per year.
Answer:
210 CM when she moved in
33 CM is the growth rate
Step-by-step explanation:
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