Exam 5: Growth and Decay: An Introduction to Exponential Functions

In 1923, a year-old Model T automobile was purchased for $750. In 1927, it was worth $450. (Note: t = 0 in 1922). Find a function which gives the value of the car, V, as a function of y, the number of years after 1922, assuming the value of the car depreciated... A) Linearly. (Write your answer in form and round values to 2 decimal places.) B) Exponentially (Write your answer in form and round values to 2 decimal places.)

An investment is originally worth $19,000 and its worth increases by a factor of 1.008 each month. Find a formula that gives the investment's worth , W, as a function of the months, m, since the original investment. Write your answer in form .

Find the growth/decay factor (assuming exponential growth/decay) for a population that decreases from 29,000,000 to 24,940,000 in one year.

Choose the function of an exponential function where and for every unit increase in x, the output is multiplied by 2.1.

Write a function in the form for an exponential function with an initial value of 50 whose output triples for each unit increase of the input.

An institution promises that investments in their mutual funds will double every 8 years. If $5,000 is invested, how much will the investment be worth in 24 years?

Compared to the function whose graph is given as a solid curve, what can you definitely say about the exponential function whose graph is dashed?

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Find the doubling time to the nearest year.

Pat recently inherited a large amount of money and wants to put some away for her child's college education. Pat figures her daughter will need $28,000 for college at age 18. Her daughter is now 8 years old and Pat can invest the money at 11.1% compounded annually. How much should Pat invest now to reach her goal? (Round the answer to the nearest penny.)

A bank compounds interest monthly at 5.1%. Choose the formula that represents the value of $1600 invested for T years.

The cost of college tuition increases about 3.2% each year. If the average cost of tuition is $9,500 in 2007, find: A) a function that gives the average tuition, T, as a function of the years after 2007, y, (Write your answer in form.) and, B) use the function to find the average cost of tution in 2012. Round your answer to the nearest dollar.

Suppose a town's population grows from 85,000 to 385,000 over 12 years. Find A) the 12-year growth factor and B) the annual growth factor. Round answers to 2 decimal places.

Given the functions: Which functions are mirror images of each other across the x-axis? Select all that apply.

Find the equation of the given function. Give your answer in or form.

Find an exponential function, , such that and for every unit increase in x, the output increases by 40 percent.. Enter your answer in form.

The following function gives the amount, A, of a radioactive element remaining as a function of y, the years of decay: Find the half-life to the nearest year.

Given the functions: Which functions have the same y-intercept? Select all that apply.

Find an exponential function with initial value 3.9 and growth rate 1.2. Write your answer in form.

The following function gives the amount, A, of a radioactive element remaining as a function of y, the years of decay: Use the "Rule of 70" to estimate the half-life to the nearest year.

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Find the doubling time.