question\nwrite an exponential function in the form $y = ab^x$ that goes through the points $(0, 16)$ and…

question\nwrite an exponential function in the form $y = ab^x$ that goes through the points $(0, 16)$ and $(5, 512)$.

question\nwrite an exponential function in the form $y = ab^x$ that goes through the points $(0, 16)$ and $(5, 512)$.

Answer

Explanation:

Step1: Solve for $a$ using $(0,16)$

Substitute $x=0$, $y=16$ into $y=ab^x$: $16 = ab^0$ Since $b^0=1$, we get $a=16$.

Step2: Substitute $a$ and $(5,512)$

Now use $a=16$, $x=5$, $y=512$: $512 = 16b^5$

Step3: Isolate $b^5$

Divide both sides by 16: $\frac{512}{16} = b^5$ $32 = b^5$

Step4: Solve for $b$

Take 5th root of both sides: $b = \sqrt[5]{32} = 2$

Answer:

$y = 16(2)^x$