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Sagot :
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.
[tex]H(t)=\sqrt{kt} + 1[/tex]
[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 = [tex]\frac{[H(t)-1]^2}{t}[/tex]
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,
[tex]k=\frac{[51-1]^2}{16}[/tex]
[tex]k=\frac{50}{16}[/tex]
[tex]k=3.125[/tex]
Therefore, value of the constant 'k' will be 3.125.
Learn more about the functions here,
https://brainly.com/question/16590698?referrer=searchResults
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