Applications of Logarithms and Exponential

Identify the percent (%) increase or decrease for the following function.

f(x) = 35 (1 – 0.06)^x

• Increase by 6%

• Decrease by 0.06%

• Increase by 0.06%

• Decrease by 6%

Identify the percent (%) increase or decrease for the function below:

f(x) = 3000 (1.17)^x

• Increase by 0.17%

• Increase by 17%

• Decrease by 17%

• Decrease by 0.17%

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

• $15,415.94
• $15,683.28
• $15,927.56
• $16,109.05

Juan purchases a $24,000 car. The value of the car is depreciating by 12.5% per year. What is the value of the car, to the nearest hundred dollars, in five years?

• $22,500

• $19,400

• $43,200

• $12,900

Judith puts $5000 into an investment account with interest compounded continuously. Which approximate annual rate is needed for the account to grow to $9110 in 30 years?

• .022%

• .02%

• 2.2%

• 2%

An online shop started its business with 15 sales per week. If their sales increased by 18% each week, use an exponential growth model to find the week during which they reached 1000 sales per week.

• They reached 1000 sales per week in the 24th week

• They reached 1000 sales per week in the 25th week

• They reached 1000 sales per week in the 26th week

In New York the minimum wage has grown exponentially. In 1966, it was $1.25 an hour and in 2015 it was $8.75. What is the rate of growth to the nearest percent?

• .04%

• 4%

• 40%

• none of the above

The average price of gas in a Texas city in 2006 was $3.92. In the same city in 2017, the average price of gas was $2.36. Using a continuous exponential decay model, find its decay rate. (Remember, continuous is A=Pe^rt)

• 60% decay

• 4.6% decay

• 50% decay

• 5.74% decay

A deposit of $1000 is made into an account that accrues interest compounded continuously (A=Pe^rt). After 14 years, the account has a balance of $2857.65. If there are no additional deposits or withdrawals, find the interest rate.

• 1.05% Interest

• 2.85% Interest

• 7.5% Interest

• 8.4% Interest