3 years ago

(710^5)(3*10^2) answer in standard form

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

210000000 you welcome ... I think that’s the answer
Scientific notation is 2.1 10^8

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Arisa [49]

Answer: $f(x)=2(0.5)^x$

Step-by-step explanation:

Given, the exponential function $y = ab^x$ for a graph that includes (–3, 16) and (–1, 4).

On putting these points, we will have

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$\dfrac{f(-3)}{f(-1)}=\dfrac{16}{4}=\dfrac{ab^{-3}}{ab^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b^{-3}}{b^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b}{b^3}=\dfrac{1}{b^2}\\\\\Rightarrow\ b^2=\dfrac{1}{4}\\\\\Rightarrow\ b=\pm\dfrac{1}{2}=\pm0.5$

since the multiplicative factor cannot be negative, so b= 0.5.

At b= 0.5

$4=a(0.5)^{-1}\\\\\Rightarrow\ 4=a(\dfrac{1}{2})^{-1}\\\\\Rightarrow\ 4=a(2)\\\\\Rightarrow \ a=2$

So, the required function is $f(x)=2(0.5)^x$ .

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