Exponential Growth and Decay: Algebra 1 Math Test – PDF Download

Question 1: Table to equation (2 points)

The table shows an exponential function.

1. Find the constant factor. (1 point)
2. 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.

1. \(x=1,2,3,4\) and \(y=5,10,15,20\) (1 point)
2. \(x=1,2,3,4\) 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.

1. \(y=1500(1.06)^{t}\) (1 point)
2. \(y=60(0.75)^{t}\) (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.

1. State \(a\) and \(b\). (1 point)
2. Write the equation. (1 point)
3. What happens to \(y\) as \(x\) gets larger? (1 point)

Question 6: Compound interest (3 points)

Maya deposits $3,000 in an account that pays 4% interest compounded quarterly. The formula is \(A=P(1+\frac{r}{n})^{nt}\).

1. Substitute the values for 2 years. (1 point)
2. Find the balance after 2 years, to the nearest cent. (1 point)
3. 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.

1. Which curve is the exponential function? Give a reason. (1 point)
2. For which whole number \(x\) does the exponential first have the greater value? Show the values. (1 point)
3. 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.

1. Explain what 1200 and 1.15 mean in this situation. (1 point)
2. Find the subscribers after 3 months, to the nearest whole number. (1 point)

⬇ Download the Algebra 1 Exponential Growth and Decay test (PDF, 91 KB)

See every chapter on the Algebra 1 math page.