MATH SOLVE

2 months ago

Q:
# When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? a) 3/10 b) 2/5 c) 1/2 d) 2/3 e) 6/5

Accepted Solution

A:

Answer:Option D is the correct answer.Step-by-step explanation:Initial height = 4 feetGiven that the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.Let the rate of growing each year be g.After 6 years height of tree = 4 + 6gAfter 4 years height of tree = 4 + 4gAt the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.That is [tex]4+6g=4+4g+\frac{4+4g}{5}\\\\4+6g=\frac{20+20g+4+4g}{5}\\\\20+30g=24+24g\\\\6g=4\\\\g=\frac{2}{3}ft/year[/tex]Option D is the correct answer.