Question
3. Given : \( g(x)=k^{x} \) find \( k \), if \( g \) passes through \( (5 ; 32) \)
Ask by Vaughan Norton. in South Africa
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( k = 2 \)
Solution
1. Substitute the given point into the function:
\[
g(5) = k^5 = 32
\]
2. Solve for \( k \) by taking the fifth root of both sides:
\[
k = \sqrt[5]{32}
\]
3. Recognize that \( 32 = 2^5 \). Thus:
\[
k = \sqrt[5]{2^5} = 2
\]
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Simplify this solution Extra Insights
To find \( k \) in the function \( g(x) = k^x \) that passes through the point \( (5, 32) \), you plug in the coordinates into the equation. This gives you: \[ g(5) = k^5 = 32 \] Next, rewrite 32 as \( 2^5 \): \[ k^5 = 2^5 \] By equating the bases, you find that \( k = 2 \). So, the function is \( g(x) = 2^x \). Isn’t it fun how these mathematical relations lead us to uncover \( k \)? Now you have \( g(x) \) all set up!
