Question

Jason made an initial deposit of $4,000 into a savings account that gains 1% interest each year. Using the inequality below, determine the number of years, x, when the amount in the savings account will be greater than $4,832.44.

$4,000(1.01)^x > $4,832.44

A) 8 years
B) 6 years
C) 10 years
D) 12 years

Answer 1

To determine the number of years when the amount in the savings account will be greater than $4,832.44, we can solve the inequality: $4,000(1.01)^x > $4,832.44. The number of years, x, when the amount in the savings account will be greater than $4,832.44 is approximately 8 years.

Step-by-step explanation:

To determine the number of years when the amount in the savings account will be greater than $4,832.44, we can solve the inequality:

$4,000(1.01)^x > $4,832.44

First, divide both sides of the inequality by $4,000:

(1.01)^x > 1.20811

Next, take the logarithm (base 1.01) of both sides to isolate the exponent:

x > log1.01(1.20811)

Using a calculator, we find that log1.01(1.20811) is approximately 7.42.

Therefore, the number of years, x, when the amount in the savings account will be greater than $4,832.44 is approximately 8 years