Applying and analysing exponential and logarithmic functions

You invested $400 into an account with 7.5% interest rate compounded monthly. Which equation can be used to calculate how much you will have in 7 years?

• $f\left(x\right)\ =\ 7.5\left(1+\frac{400}{100}\right)^7$

• $f\left(x\right)\ =\ 400\left(1+\frac{7}{100}\right)^{7.5}$

• $f\left(x\right)\ =\ 400\left(1+\frac{7.5}{100}\right)^7$

• $f\left(x\right)\ =\ 7\left(1+\frac{7.5}{100}\right)^{400}$

A green energy campaign is trying to convince households in a target area to switch from incandescent to florescent lightbulbs. There are 241,224 households in this target area.

Initially 184 households make the change. Market research indicates that, in the absence of limiting factors, we could increase that number by 20% each month.

What is r, the intrinsic exponential growth rate, for a logistic model of this situation?

Round to 3 decimal places.

Use the function, N = 14,000(.96)^t. Where N is the number of employees and t is the number of years.
How many employees will there be after 3 years?

• 14,000 employees
• 12,386 employees
• 40,360 employees
• 15,748 employees

The student council makes an initial investment in a savings account that earns interest.  The value of the savings account after m months is determined by the function v(m) = 2,000(1.005)^m.  What is the interest rate of the savings account?

• 2,000
• 1.005
• .005
• .5%

Gina buys a car for $13,500. Assume its value will decrease by about 15% per year. Write an exponential function to model the value of the car. Graph the function. When will the value fall below $3,000.

• The car's value will fall below $3,000 after 7 years.

• The car's value will fall below $3,000 after 8 years.

• The car's value will fall below $3,000 after 9 years.

• The car's value will fall below $3,000 after 10 years.

For which of the following expressions would you have to MULTIPLY the exponents in order to simplify it?

Principal: $5000 Interest Rate: 2.75% Time: 25 years Compounded Monthly State the future account balance.

• $9935.87

• $10,749.30

• $12,657.59
• $12550.84

Chris borrows $450 from Gavin. Gavin lets Chris choose either a simple interest loan for 10 years with a 3.5% interest rate or a loan compounded annually for 7 years with a 2% interest rate. Which should Chris choose if he wants the cheaper plan? Use I=P*r*t for simple interest (make sure to add I plus P at the end) and A=P*(1+r)^t for compound interest.

• The simple interest plan

• The compound interest plan

The Mendez family just bought a home for $180,000. If the value of the home increases by 3% per year, use an exponential function to find the value of the home after 10 years.

• $258,000

• $250,000

• $242,000

• $234,000

Michael has $10 in his savings account. Option 1 will add $100 to his account each week. Option 2 will double the amount in his account at the end of each week. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option(s) will enable him to reach his goal.

How should you answer this question?

• yes or no

• Option 1, Option 2, neither, or both

• write an equation

• how much money he has in his account after 7 weeks