Exercise 41 Page 304

We are given the equation y=2^(x+2) representing the size of a new photo compared to the original after x enlargements. Since we want the new photo to be 32 times the size of the original, we will substitute 32 for y and solve for x to find the amount of enlargements.

y=2^(x+2)

Substitute

y= 32

32=2^(x+2)

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Solve for x

Rewrite

Rewrite 32 as 2^5

2^5=2^(x+2)

EquateExponents

Equate exponents

5=x+2

SubEqn

LHS-2=RHS-2

3=x

RearrangeEqn

Rearrange equation

x=3

We have found that the photo must be enlarged 3 times.