Question

The membership fee at a sports club was $600 per year. Each year, the membership fee increased by 7%. The cost of membership, y, can be modeled by the equation y=600(1.07)^x, where x is the number of years.

How many years will it take for the cost of the membership to be $900?

Choose the answer that gives the correct logarithmic equation and answer.


x=log1.5(1.07)

x=6


x=log1.07(1.5)

x=6


x=log(1.51.07)

x=1


x=log(1.071.5)

x=1

Answer 1

The correct logarithmic equation to determine the number of years for the membership fee to increase to $900 is x = log1.07(1.5), and the number of years is x = 6.

Step-by-step explanation:

To find out how many years it will take for the cost of the sports club membership to reach $900, we need to solve the equation y = 600(1.07)x for when y is equal to 900. We set up the equation:

900 = 600(1.07)x

Dividing both sides by 600 gives:

1.5 = (1.07)x

To solve for x, we take the logarithm of both sides:

log(1.5) = x log(1.07)

Then, dividing both sides by log(1.07) gives the answer:

x = log(1.5) / log(1.07)

This corresponds to the correct logarithmic equation and answer:

x = log1.07(1.5)

x = 6

Therefore, it will take 6 years for the membership fee to increase from $600 to $900.