Answer:
Given that,
In 1980, James planted a tree that was 1 foot tall.
In 1996, that same tree was 71 feet tall.
James finds that the height of the tree can be modeled by H(t),
[tex]H(t)=\sqrt{kt}+1[/tex]where H (t) is the height of the tree in feet, t is the number of years since 1980.
To find the value of k.
Explanation:
Since it is given that, In 1980, James planted a tree that was 1 foot tall.
when t=0, we get the height of the tree as,
[tex]H(t)=1[/tex]Therefore, t is the number of years since 1980.
we have that, In 1996, that same tree was 71 feet tall.
t=1996-1980
t=16
and H(t)=71.
Substitute these values in the given equation we get,
[tex]71=\sqrt{16\times k}+1[/tex][tex]71-1=4\sqrt{k}[/tex][tex]70=4\sqrt{k}[/tex][tex]\sqrt{k}=\frac{70}{4}[/tex][tex]\sqrt{k}=17.5[/tex][tex]k=17.5^2[/tex][tex]k=306.25[/tex]The value of k is 306.25
Answer is: 306.25
