Ellen is playing a video game in which she captures butterflies. there are 3 butterflies on screen, but the number of butterflies doubles every minute. after 4 minutes, she was able to capture 7 of the butterflies. part a. write an expression for the number of butterflies after 4 minutes. use a power of 2 in your answer. part b. write an expression for the number of butterflies remaining after ellen captured the 7 butterflies. simplify the expression.

Answer 32

when a number doubles, it is simply a higher power of 2  

so there are 3 butterflies in the beginning, which can also be written as 3 * (2^0) where the 0 is the initial power, since anything to the 0 power is 1 (except for 0)  

so the expression would be 3 * (2^n)  

after 4 minutes, it would be 3 * (2^4) or 3 * 16 or 48  

to find out how many are remaining, we know that she captured 7 of them, so it would be 3 * (2^4) - 7  

for question 2, Jeff texts 4 classmates, and then they each text 4 classmates, so that would be 4^2 or 16, but since 2 people do it, it would be

32

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