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3 years ago

Please help!! Which values of a and b in the exponential function y=a*b^x would result in the following graph?

Mathematics

1 answer:

Masja [62]3 years ago

4 0

Answer: $a=-3, b=2$

Step-by-step explanation:

1. To solve this problem substitute the values of $a$ and $b$ into the function $y=a*b^{x}$ and prove for the value $x=0$ .

2. When $x=0$ , $b^{0}=1$ and $a*1=a$ ; this means that the graph of the function should cut in the axis $y=a$ , if this does not happen, the values of $a$ and $b$ are not the right ones.

3. Then, we conclude that the correct option is the Option A:

$y=a*b^{x}$

$y=-3*2^{0}$

$y=-3$

4. You can see that the function cut the y-axis at -3.

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Let $R$ be the solid. Then the volume is

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which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
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and

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$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
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