GreenlightTestPrep wrote:

On July 1, 2017, a certain tree was 128 centimeters tall. Each year, the tree's height increases 50%.

Given this growth rate, the tree's height on July 1, 2023 will be how many centimeters greater than the tree's height on July 1, 2022?

A) (2^2)(3^4)

B) (2)(3^4)

C) (2)(3^5)

D) (4)(3^5)

E) (2)(3^6)

Let's create a

growth table and look for a

patternyear | height in cm2017: 128

2018: 128(1.5)

2019: 128(1.5)^2

2020: 128(1.5)^3

2021: 128(1.5)^4

2022:

128(1.5)^52023:

128(1.5)^6The tree's height on July 1, 2023 will be how many centimeters greater than the tree's height on July 1, 2022? Difference =

128(1.5)^6 -

128(1.5)^5Factor out 128(1.5^5) to get: difference = 128(1.5^5)[1.5 - 1]

Simplify: difference = 128(1.5^5)[0.5]

Rewrite with fractions: difference = (2^7)(3/2)^5)(1/2)

Expand: difference = (2^7)(3^5)/(2^6)

Simplify: difference = (2)(3^5)

Answer: C

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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