Algebra 2 Exponential Models Quiz – Free PDF

Contents

This algebra 2 exponential models quiz asks 10 multiple-choice questions on exponential functions and the number e, and each answer comes with a short explanation.

Ten multiple-choice questions on exponential growth and decay, compound interest, the number e, half-life, and doubling time. Choose the single best answer. Each explanation shows the key step and the most common mistake.

Algebra 2Common Core: F-IF.C.8b · F-LE.A.4 · F-LE.B.5

🎯 Exponential Functions and the Number e – Algebra 2 math quiz

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Question 1

A quantity grows 7% each year. What is the yearly growth factor $b$?

A $b=0.07$

B $b=0.93$

C $b=1.07$

D $b=7$

Question 2

A medicine loses 12% of its concentration each hour. What is the hourly factor $b$?

A $b=1.12$

B $b=0.88$

C $b=0.12$

D $b=12$

Question 3

Which equation matches the graph?

The graph of an exponential function.

A $y=3\cdot 2^{x}$

B $y=2\cdot 3^{x}$

C $y=3\cdot 0.5^{x}$

D $y=3x+3$

Question 4

Find the balance of $500 at 6% compounded annually for 3 years.

A $590.00

B $595.51

C $598.34

D $631.24

Question 5

Which value is closest to the number $e$?

A about 3.142

B about 1.618

C about 2.178

D about 2.718

Question 6

Which formula gives the balance with continuous compounding?

A $A=P(1+r)^{t}$

B $A=P\left(1+\frac{r}{n}\right)^{nt}$

C $A=P+rt$

D $A=Pe^{rt}$

Question 7

What is the half-life of the quantity shown?

A decaying quantity.

A 8 hours

B 4 hours

C 24 hours

D 12 hours

Question 8

How long does it take money to double at 3% interest compounded yearly?

A 23.45 years

B 33.33 years

C 24.00 years

D 66.67 years

Question 9

About how long does the balance in the graph take to reach $2,000?

A balance A(t) = 1,000(1.05)ᵗ and the line A = 2,000.

A about 7 years

B about 20 years

C about 14 years

D about 28 years

Question 10

Solve $5\cdot 3^{t}=45$ for $t$.

A $t=9$

B $t=3$

C $t=2$

D $t=15$

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

y = a·bᵗ: a is the initial value and b is the factor per period.
Percent rate r gives b = 1 + r for growth and b = 1 − r for decay.
Compound interest: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt) with e ≈ 2.71828.
Half-life model: A = A₀(1/2)^(t/h); doubling time at rate r is ln 2 ÷ ln(1 + r).
To solve a·bᵗ = d for t, isolate bᵗ and take a logarithm: t = ln(d/a) ÷ ln b.