Exam 3: Linear and Exponential Change: Comparing Growth Rates

An investment is growing by 9% each year. How long does it take the investment to double in value?

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. How long will it take for the jacket to cost $200 dollars?

Suppose you are at the base of a hill, and you see a sign that reads "Elevation 4000 feet." The road you are on goes straight up the hill to the top, where you see another sign that reads "Elevation 4500 feet." If the top of the hill is 5 horizontal miles from the base, what is the growth rate in your elevation with respect to horizontal distance as you drive up the road?

What is the number of distinct real solutions for the equation ?

The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every degree of rise in temperature, the speed of sound increases by 1.1 feet per second. At 67 degrees the speed of sound is _____ feet per second.

A rectangular playground has the dimensions 20 yards by 30 yards. You want to double the space by adding the same amount to both the length and width. What is the perimeter of the expanded playground?

The _____ of a radioactive substance is the time it takes for half of the substance to decay.

The acidity of a solution is determined by the concentration H of hydrogen ions. The formula is . The accompanying exponential formula is H = 0.1^pH. Lower pH values indicate a more acidic solution. Normal rain has a pH of 5.6. Suppose acid rain has a pH of 4.3. How many times as acidic as normal rain is this?

Which of the following is a quadratic function?

You have a 400-foot roll of fencing to enclose a playground. If you want to construct a rectangular playground, what is the largest possible area of the playground?

For the linear function y = mx + b, each 1-unit increase in x corresponds to a change of _____ unit(s) in y.

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. When the sound of a speaker is recorded as 80 decibels at 10 feet, what is the decibel reading if four identical speakers are added at 20 feet?

Radium-226 is subject to radioactive decay, and each year the amount present is reduced by 4.2%. The amount of radium-226 is an exponential function of time in years. What is the base of this exponential function?

If we drop a rock near the surface of Earth, its velocity increases by 32 feet per second for each second the rock falls. If v is the velocity in feet per second and t is the time in seconds:

From 1929 to the early 1930s, the prices of consumer goods actually decreased. Economists call this phenomenon deflation. The rate of deflation during this period was around 7% per year. Suppose this rate of deflation persisted over 20 years. What would be the cost after 20 years of an item that cost $500 initially?

Which of the following statements is NOT correct for the function ?

A small business has the following revenue and cost functions for a product: and . If the break-even point lies where revenue equals cost, how many break-even points are there?

The probability P (as a decimal) that a tsunami with waves over 15 feet high will NOT strike a beach community over a period of t years is given by the formula P = 0.93^t. What is the probability that someone living in the beach community for 20 years will NOT encounter a tsunami with waves 15 feet or higher?

An increase of 1 on the pH scale causes acidity to be multiplied by a factor of 0.1, while a decrease of 1 on the pH scale causes acidity to be multiplied by a factor of 10. If pure water has a pH of 7, how many times as acidic as pure water is a solution measuring a pH of 3?

Initially, a population is 750, and it grows by 3% each year. Find a formula for the population, P, at any time, t.