Question

The 1997 a value of an object was $5000. In 2012 , it was worth $9500. The annual percent growth has been constant. What is the annual percent growth?

A) 1.37%
B) 2.37%
C) 3.37%
D) 4.37%

Answer 1

D. 4.37 %

Step-by-step explanation:

Around 1997 the value of the object was $5000 . it later worth $9500 in the year 2012. The period in time from 1997 to 2012 is roughly 15 years. The amount increased by 9500 - 5000 = $4500.

The annual percentage growth is constant . That means the percentage growth for each year is constant. The annual percentage growth can be computed as follows:

f = final value

i = initial value

years difference = y

((f / i)∧ 1/y - 1) × 100

f = 9500

i = 5000

(9500/5000)∧ 1/15 - 1

(1.9)∧1/15 - 1

(1.9)∧ 0.06666667 - 1

1.0437189836 - 1 = 0.0437189836

convert to percentage

0.0437189836 × 100 = 4.3718983645

Annual percentage growth = 4.37 %

Answer 2

Given:
1997 - 5,000
2012 - 9,500

9,500 - 5,000 = 4,500
2012 - 1997 = 15 years

(9,500/5,000)^1/15 - 1
1.9^1/15 - 1
1.043718 - 1 = 0.043718
0.043718 * 100% = 4.3718%

The answer is D.) 4.37%