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.

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

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

[tex]Number \of\ Butterflies\ after\ n\ minutes = 3*2^n[/tex]

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.

[tex]Number \of\ Butterflies\ after\ n\ minutes = 3*2^n[/tex]

So, after 4 minutes

[tex]Number \of\ Butterflies\ after\ 4\ minutes = 3*(2)^4[/tex]

[tex]Number \of\ Butterflies\ after\ 4\ minutes = 3*(16)[/tex]

[tex]Number \of\ Butterflies\ after\ 4\ minutes = 48[/tex]

As Ellen has captured 7 butterflies, So:

[tex]Number \of\ Butterflies\ remaining = 48-7[/tex]

[tex]Number \of\ Butterflies\ remaining = 41[/tex]

tecumismael tecumismael · Answer 2 · 2021-03-02T15:10:45+01:00

tecumismael tecumismael

02-03-2021

Answer is 4 x 4

Step-by-step explanation:

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