First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

$y=2^x\\\ln(y)=x \ln(2)$

Implicitly differentiate the left side and take the derivative of the right side

$\frac{y'}{y} =\ln(2)$

Multiply both sides by 'y' which was defined as 2^x

$y'=\ln(2)*2^x$

Plug in x = 2 and x = 3 to see which slope is larger

$y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)$

4 0

3 years ago

Help me with this hw please

zvonat [6]

Answer:

12 = 3 + p

Step-by-step explanation:

She has a total of 12 pencils

3 of them are red

The rest are "p"

p + 3 must equal 12 because she has a total of 12 pencils consisting of 3 red and "p" as the rest

3 0

2 years ago

How many solutions does x2 = 9 have?

MrRa [10]

It should have 2 solutions

5 0

2 years ago

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