Unit 2 check

Unit 2 check: Exponential and Logarithmic Functions

15 questions from 15 lessons in Unit 2. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 2.1 · Multiple choice

No calculator. A tile pattern grows in steps. Step 0 has 5 tiles, and each step adds 3 more. Let $a_{n}$ be the number of tiles in step $n$ . Which describes the graph of $a_{n}$ for steps 0 through 6?

Question 2 · from 2.2 · Match

No calculator. Tap a function, then how it starts and how it changes for each unit of $x$ .

Question 3 · from 2.3 · Fill the statement

No calculator. Tap a blank, then tap an answer.

$\lim_{x \to \infty} 4 (0.5)^{x}$ is , and $\lim_{x \to - \infty} 4 (0.5)^{x}$ is .

Setup for question 4

Three students each wrote a form of the same function $f$ . All three forms are equivalent.

Three equivalent forms of $f (x)$
Form	$f (x)$
P	$2 \cdot 2^{x}$
Q	$\frac{1}{2} \cdot 4^{\frac{x}{2} + 1}$
R	${(\frac{1}{2})}^{- x - 1}$

Question 4 · from 2.4 · Spot the error

No calculator. A fourth student rewrites Form R with base 2. Tap the first line with a mistake.

Setup for question 5

A nurse records the amount of a medicine left in a patient's bloodstream every hour after a dose. The ratios of consecutive readings sit between about 0.84 and 0.87, close to constant but not exactly, which is what real measurements look like. That makes this a job for an exponential regression. Enter the hours and the amounts as two lists and run ExpReg, which reports a model $y = a b^{x}$ .

Medicine in the bloodstream
$t$ (hours)	$A (t)$ (milligrams)
0	250
1	212
2	181
3	152
4	131
5	110
6	94

Question 5 · from 2.5 · Calculate

Graphing calculator required. An exponential regression on medicine data (250, 212, 181, 152, 131, 110 and 94 milligrams at $t = 0$ to 6 hours) gives $A (t) = 249.88 (0.8494)^{t}$ . After how many hours does the model first give 50 milligrams? Give your answer to the nearest tenth of an hour.

Your answer hours

Setup for question 6

During a flu outbreak a clinic counts the patients it sees each day. It fits a linear model $L (d)$ and an exponential model $E (d)$ , where $d$ is days since the count began. The table gives each model's prediction next to the actual count. The clinic schedules its nurses from the forecast.

Patients per day, actual and predicted (invented data)
$d$ (days)	Patients	$L (d)$	$E (d)$
0	12	7.75	12.06
1	16	15.21	15.66
2	20	22.68	20.33
3	26	30.14	26.39
4	35	37.61	34.26
5	44	45.07	44.48
6	58	52.54	57.75

Question 6 · from 2.6 · Multiple choice

No calculator. Find the sign of each residual (actual minus predicted) of the linear model $L$ , in order of day. Is $L$ an appropriate model for these data?

Setup for question 7

The function $f$ is defined only at the five inputs in the table. The graph of $g$ is a line, and the marked points on it are at the whole-number inputs from $- 1$ to $5$ .

Values of $f$
$x$	$- 2$	$0$	$1$	$2$	$4$
$f (x)$	$5$	$- 1$	$4$	$6$	$2$

Graph of $g$

The line through the marked points is the graph of $g$ .

Question 7 · from 2.7 · Multiple choice

No calculator. Which point is on the graph of $y = f (g (x))$ ?

Setup for question 8

The table gives every value of a function $f$ . Its domain is just these five inputs, and no output repeats, so $f$ is invertible.

Values of $f$
$x$	$f (x)$
−3	11
−1	6
0	4
2	−1
5	−3

Question 8 · from 2.8 · Calculate

No calculator. What is $f^{- 1} (- 1)$ ?

Your answer

Question 9 · from 2.9 · Put it in order

No calculator. Put the values in order from least to greatest.

Question 10 · from 2.10 · Spot the error

No calculator. A student simplifies four expressions, one per line. Tap the line with the mistake.

Question 11 · from 2.11 · Multiple choice

No calculator. Let $f (x) = - 3 \log_{4} x$ . Which gives the domain and range of $f$ ?

Setup for question 12

The table gives three values of a logarithmic function $q (x) = \log_{b} x$ , rounded to three decimal places. The base $b$ is greater than 1, and you do not need to know it.

Selected values of $q (x) = \log_{b} x$
$x$	$q (x)$
2	0.356
3	0.565
5	0.827

Question 12 · from 2.12 · Calculate

No calculator. Use the table of $q (x) = \log_{b} x$ to find $q (18)$ . Give a decimal.

Your answer

Question 13 · from 2.13 · Decide and justify

No calculator. Which describes every solution of ${0.7}^{x} > 0.2$ ?

Which reason supports your answer?

Question 14 · from 2.14 · Decide and justify

No calculator. A logarithmic regression on a data set gives $y = 12.4 + 3.1 \ln x$ . Which expression gives the input at which the model's output is 25?

Which reason supports your answer?

Question 15 · from 2.15 · Spot the error

No calculator. A student turns a semi-log line back into an exponential model. Tap the line where the mistake is first made.

0 of 15 answered.