Question

Ellen is playing a video game in which she captures butterflies. There are 3 butterflies onscreen, but the number of butterflies doubles every minute. After 4 minutes, she was able to capture 7 of the butterflies.
A)LOOK FOR A PATTERN. Write an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer.
B)Write an expression for the number of butterflies remaining after Ellen captured the 7 butterflies. Evaluate the expression.

Answer 1

Answer:

A) The expression is given by $3*2^n$.

B) The remaining butterflies after Ellen captures 7 butterflies is 41.

Step-by-step explanation:

A) As the number of butterflies keeps doubling every minute so the repeating number is 2 thus we use the term $2^n$ where n given the number of minutes passed.

Initially there were 3 butterflies on the screen so we multiply the term $2^n$ with the initial number of butterflies $3$. So the expression becomes:

             $Number \of\ Butterflies\ after\ n\ minutes = 3*2^n$

B) After 4 minutes Ellen captures 7 butterflies from the total, So we subtract the term 7 from the number of butterflies we calculated through the expression.

           $Number \of\ Butterflies\ after\ n\ minutes = 3*2^n$

So, after 4 minutes

           $Number \of\ Butterflies\ after\ 4\ minutes = 3*(2)^4$

           $Number \of\ Butterflies\ after\ 4\ minutes = 3*(16)$

           $Number \of\ Butterflies\ after\ 4\ minutes = 48$

As Ellen has captured 7 butterflies, So:

            $Number \of\ Butterflies\ remaining = 48-7$

            $Number \of\ Butterflies\ remaining = 41$