Precalculus Exponential Functions and the Number e Test Solutions and Scoring (PDF)

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

Cover of the book Precalculus Math Tests with Answer Keys (PDF)

Download as a PDFThe Precalculus tests book with answer keysPrintable PDFSee the book ›

Sommaire

This exponential test answers 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.

Worked solutions and scoring notes for the 9-question exponential functions test. Use the scoring line under each solution to award partial credit.

Precalculus · Common Core State Standards: F-LE.A.2, F-IF.C.8b, F-LE.B.5, F-IF.C.7e

Exponential test answers: worked solutions

Question 1 – Evaluate and classify [2 pts]

$f(3)=250(0.512)=128$. The base $0.8=1-0.2$.

$128$; decay at $20\%$

Scoring: 1 point for f(3), 1 point for decay and the rate.

Question 2 – Write from points [2 pts]

$a=4$. $4b^{2}=36$, so $b^{2}=9$ and $b=3$.

$y=4\cdot3^{x}$

Scoring: 1 point for a, 1 point for b.

Question 3 – Population model [2 pts]

$P(t)=12000(1.025)^{t}$. $P(8)\approx 14{,}621$.

$P(t)=12000(1.025)^{t}$; about $14{,}621$

Scoring: 1 point for the model, 1 point for the value.

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

Shifted left 1 and down 3: asymptote $y=-3$. $y(0)=2-3=-1$.

$y=-3$; $(0,-1)$

Scoring: 1 point each.

Question 5 – Model from a graph [3 pts]

f(4) = 10.125.

(a) $a=2$, $b=\frac32=1.5$. (b) $50\%$. (c) $2(1.5)^{4}=2(5.0625)=10.125$.

$a=2,\ b=1.5$; $50\%$; $10.125$

Scoring: 1 point for each part.

Question 6 – Compound interest [2 pts]

$3000(1.005)^{60}\approx \$4{,}046.55$.

$\$4{,}046.55$

Scoring: 1 point for the setup, 1 point for the value.

Question 7 – Continuous compounding [2 pts]

$1500e^{0.4}\approx \$2{,}237.74$.

$\$2{,}237.74$

Scoring: 1 point for the setup, 1 point for the value.

Question 8 – Half-life [3 pts]

Half remains at t = 8; 15 g at t = 24.

(a) $120\left(\frac12\right)^{3}=15$. (b) $120\cdot2^{-1/2}\approx84.85$. (c) $60$ is half of $120$, so $t=8$.

$15\text{ g}$; $84.85\text{ g}$; $8$ days

Scoring: 1 point for each part.

Question 9 – Which earns more? [2 pts]

Yearly: $1000(1.06)^{10}\approx \$1{,}790.85$. Continuous: $1000e^{0.59}\approx \$1{,}803.99$.

Continuous: $\$1{,}803.99$ is greater than $\$1{,}790.85$

Scoring: 1 point for each value with the correct comparison in the second point.

Total score

Total

20 points

Key facts behind this exponential test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF