Modeling with Exponential and Logarithmic Equations — Unit test Answers

What is the range of the function graphed below?

What is the true solution to the logarithmic equation?

If and , what is the degree of ?

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?

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

A savings account pays 2% interest compounded annually. If $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit?

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?

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of ?

Which function is shown in the graph below?

Which function has a horizontal asymptote of y = 3?

Which of the following shows the graph of y = –(2)x – 1?

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?

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?

Which is the graph of ?

What is the range of the function f(x) = –2(6x) + 3?