Question

In 1980, James planted a tree that was 1 foot tall.the radical function H (t)In 1996, that same tree was 71 feet tall. James finds that the height of the tree can be modeled byWhat is the value of k?Vkt + 1, where H (t) isthe height of the tree in feet, t is the number of years since 1980, and k is a specific constant.• 816.67© 17.50• 306.25• 51.04

Answer 1

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),

$H(t)=\sqrt{kt}+1$

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,

$H(t)=1$

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,

$71=\sqrt{16\times k}+1$$71-1=4\sqrt{k}$$70=4\sqrt{k}$$\sqrt{k}=\frac{70}{4}$$\sqrt{k}=17.5$$k=17.5^2$$k=306.25$

The value of k is 306.25

Answer is: 306.25