Precalculus Exponential Functions and the Number e Test with Point Values (PDF)

Precalculus math test: Exponential Functions and the Number e – Maths PDF

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This exponential test for Precalculus covers exponential functions and the number e (Common Core F-LE.A.2, F-IF.C.8b, F-LE.B.5, F-IF.C.7e), with a free PDF to print.

This 20-point test covers exponential growth and decay, graphs, compound interest and a half-life model (F-LE.A.2, F-IF.C.8b, F-LE.B.5). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Exponential Functions and the Number e
Standards: F-LE.A.2, F-IF.C.8b, F-LE.B.5, F-IF.C.7e
Time: 45 minutes
Total: 20 points

Exponential test: questions

Question 1 – Evaluate and classify [2 pts]

For $f(x)=250(0.8)^{x}$, find $f(3)$ and state whether it is growth or decay and the percent rate.

Question 2 – Write from points [2 pts]

Write the exponential function through $(0,4)$ and $(2,36)$.

Question 3 – Population model [2 pts]

A city of $12{,}000$ grows $2.5\%$ per year. Write the model and find the population after 8 years to the nearest person.

Question 4 – Features of a transformed graph [2 pts]

Graph of y = 2^(x+1) – 3.

For $y=2^{x+1}-3$, state the horizontal asymptote and the $y$-intercept.

Question 5 – Model from a graph [3 pts]

An exponential graph.

(a) Find $a$ and $b$ in $f(x)=ab^{x}$. (b) State the percent growth rate. (c) Find $f(4)$.

Question 6 – Compound interest [2 pts]

Find the value of $\$3{,}000$ at $6\%$ compounded monthly for 5 years.

Question 7 – Continuous compounding [2 pts]

Find the value of $\$1{,}500$ at $4\%$ compounded continuously for 10 years.

Question 8 – Half-life [3 pts]

Decay of an iodine sample.

A sample of $120$ g of iodine has a half-life of 8 days, so $A(t)=120\left(\frac12\right)^{t/8}$. (a) Find $A(24)$. (b) Find $A(4)$ to the nearest hundredth. (c) Find $t$ when $A=60$.

Question 9 – Which earns more? [2 pts]

After 10 years, which is greater: $\$1{,}000$ at $6\%$ compounded yearly, or $\$1{,}000$ at $5.9\%$ compounded continuously? Compute both.

Key facts behind this exponential test

Key facts

f(x) = a b^x: a = f(0) and b = growth or decay factor.
A rate r per period gives b = 1 + r (growth) or b = 1 – r (decay).
The parent graph has the horizontal asymptote y = 0; y = a b^(x – h) + k has asymptote y = k.
Compound interest: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt).
e is about 2.71828, the limit of (1 + 1/n)^n.

How to use this exponential test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Precalculus chapters: Precalculus math.

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