Question

In 1980, James planted a tree that was 1 foot tall. In 1996, that same tree was 51 feet tall. James finds that the height of the tree can be modeled by the
radical function H (t) = v kt + 1 where H (t) is the height of the tree in feet, t, is the number of years since 1980, and k is a specific constant. What
is the value of k?

Answer 1

Divide and see what you get = 51

Answer 2

  Value of the specific constant 'k' for the given function will be 3.125.

Simplification of a function for the value of variables used:

• If a function modeling the height of a tree in 't' years is.

        $H(t)=\sqrt{kt} + 1$

        [where,  k = constant , t = Number of years]

        And we have to find the value of 'k', simplify the function in terms of 'k'.

         H(t) - 1 = √kt

         [H(t) - 1]² = kt

         k = $\frac{[H(t)-1]^2}{t}$

Given in the question,

• James planted a tree of height 1 feet in 1980.
• Same tree was 51 feet tall in 1996.

Number of years between 1980 and 1996 (t) = 16

H16) = 51 feet

Substitute the values in the expression,

$k=\frac{[51-1]^2}{16}$

$k=\frac{50}{16}$

$k=3.125$

    Therefore, value of the constant 'k' will be 3.125.

Learn more about the functions here,

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