Study on the flyACTMathematicsExponential relationships
Mathematics
Repeated multiplication by the same factor is what makes growth or decay exponential, while linear change adds the same amount at each step.
Exponential relationships are usually written as a starting amount times a base raised to the power t: a base greater than one means growth, and a base between zero and one means decay. ACT Mathematics also asks for solutions of equations such as three to the power x equals eighty-one, where writing eighty-one as three to the fourth power gives x equals four.
Answer choices often confuse the growth factor, which is the base, with the percent rate of change.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Easier
Derek invests 350 dollars in an account whose balance doubles every 7 years. If no money is added or withdrawn, what is the balance after 21 years?
Answer: A — 2,800
Twenty-one years contains 3 doubling intervals. The balance is dollars.
Question 2Mid
What is the value of that satisfies ?
Answer: D — 7
Rewriting gives . Equating exponents, , yields .
Question 3Easier
A quantity is modeled by , where is the number of years. Which of the following describes the annual percent change in the quantity?
Answer: B — increase
The growth factor 1.06 equals . Therefore, the model represents approximately a increase each year.
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
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