This algebra 1 exponential functions test checks exponential growth and decay in 45 minutes, with 8 questions for a total of 20 points.
This test covers exponential growth and decay in Algebra 1: linear and exponential tables, factors and percent rates, graphs, compound interest and interpreting parameters (F-LE and F-IF.C.8b). Eight questions are worth 20 points in total. Show every step, and round money to the nearest cent unless told otherwise.
- Grade: Algebra 1
- Chapter: Exponential Growth and Decay
- Common Core: F-LE.A.1a, F-LE.A.1c, F-LE.A.2, F-LE.A.3, F-IF.C.8b, F-LE.B.5
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 3 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts)
Algebra 1 Exponential Functions Test: questions 1–5
Question 1: Table to equation (2 points)
The table shows an exponential function.
- Find the constant factor. (1 point)
- Write the function in the form \(y=a\cdot b^{x}\). (1 point)
Question 2: Classify tables (2 points)
Tell whether each table is linear or exponential. Justify with the difference or factor.
- \(x=1,2,3,4\) and \(y=5,10,15,20\) (1 point)
- \(x=1,2,3,4\) and \(y=4,12,36,108\) (1 point)
Question 3: Growth and decay rates (2 points)
Give the starting value and the yearly percent change.
- \(y=1500(1.06)^{t}\) (1 point)
- \(y=60(0.75)^{t}\) (1 point)
Question 4: Write and use exponential models (3 points)
(a) A town of 8,000 people grows 2.5% per year. Write a function \(P(t)\) for the population after \(t\) years. (1 point)
(b) Use it to find the population after 10 years, to the nearest whole person. (1 point)
(c) A car worth $18,000 loses 12% of its value each year. Write a function \(V(t)\) for its value. (1 point)
Question 5: Reading an exponential graph (3 points)
The graph shows an exponential function.
- State \(a\) and \(b\). (1 point)
- Write the equation. (1 point)
- What happens to \(y\) as \(x\) gets larger? (1 point)
Algebra 1 Exponential Functions Test: questions 6–8
Question 6: Compound interest (3 points)
Maya deposits $3,000 in an account that pays 4% interest compounded quarterly. The formula is \(A=P(1+\frac{r}{n})^{nt}\).
- Substitute the values for 2 years. (1 point)
- Find the balance after 2 years, to the nearest cent. (1 point)
- How much interest does the account earn? (1 point)
Question 7: Exponential versus linear (3 points)
Curve A is \(y=3^{x}\) and Curve B is \(y=10x+2\). The graph shows both.
- Which curve is the exponential function? Give a reason. (1 point)
- For which whole number \(x\) does the exponential first have the greater value? Show the values. (1 point)
- Explain why the exponential stays above the line for all larger \(x\). (1 point)
Question 8: Interpret a model (2 points)
A channel’s subscriber count is \(S(t)=1200(1.15)^{t}\), where \(t\) is the number of months since launch.
- Explain what 1200 and 1.15 mean in this situation. (1 point)
- Find the subscribers after 3 months, to the nearest whole number. (1 point)
How to use this algebra 1 exponential functions test
Take this algebra 1 exponential functions test without notes, then grade it with the test answer key out of 20 points.
See every chapter on the Algebra 1 math page.
