Question

question
if $f(x)$ is an exponential function of the form of $y = ab^x$ where $f(3) = 24$ and $f(6) = 87$,
then find the value of $f(8)$, to the nearest tenth.
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answer attempt 1 out of 2
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Explanation:

Step1: Set up equations from given values

We know $f(x)=ab^x$, so:
$f(3)=ab^3=24$
$f(6)=ab^6=87$

Step2: Solve for $b$ by dividing equations

Divide the second equation by the first to eliminate $a$:
$\frac{ab^6}{ab^3}=\frac{87}{24}$
Simplify: $b^3=\frac{87}{24}=3.625$
Take cube root: $b=\sqrt[3]{3.625}\approx1.537$

Step3: Solve for $a$ using $f(3)$

Substitute $b$ into $ab^3=24$:
$a=\frac{24}{b^3}=\frac{24}{3.625}\approx6.621$

Step4: Calculate $f(8)$

Use $f(8)=ab^8=a\cdot b^6\cdot b^2$
Substitute known values:
$f(8)=87\times(1.537)^2$
Calculate $(1.537)^2\approx2.362$
$f(8)\approx87\times2.362\approx205.5$

Answer:

205.5