Modeling with Quadratic Equations — Unit test Answers

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

If , what is the value of x?

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

The amount of interest earned on an account can be represented using the recursive formula . If , and n represents the number of months the money is invested, what is the balance at the end of each month for the first three months?

What are the domain and range of ?

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

Which of the following shows the true solution to the logarithmic equation solved below?

The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

For what values of x does ?

What is the solution to

What is the range of the function graphed below?

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

Which is the graph of ?

Which recursive formula describes the sequence below?5, 13, 29, 61, 125, ...

If , what is the value of x?

Which function has a horizontal asymptote of y = 3?

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

Which function is shown in the graph below?

A sequence is defined by the explicit formula . Which recursive formula represents the same sequence of numbers?