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

2 years ago

At a school picnic, your teacher asks you to mark a field every 10 yards so students can play football. The teacher accidentally

Oxana [17]

Approximately 9 meters are in 10 yards, (as there is approximately 1 meter in a yard, .9144 to be exact.)

3 0

2 years ago

Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)

tankabanditka [31]

Step-by-step explanation:

2x²+2xy+yx+y²+2x²+2xy-yx+y²

2x²+2x²+2xy+2xy+yx-yx+y²+y²

2x²+2x²+2xy+2xy

4x²+4xy

7 0

2 years ago

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