Free Printable Unit 4a Remediation - Standard #1 Recognize Situations

1.

Increasing 5% each decade.

What is the yearly growth factor?

a)

$\frac{5\%}{10\ years}$

b)

$\frac{1.05}{10\ years}$

c)

$1.05^{\frac{1}{10}}$

d)

$5^{\frac{1}{10}}$

2.

Increasing 8% each week.

What is the growth factor each day?

a)

$\frac{8\%}{7\ days}$

b)

$\frac{1.08}{7\ days}$

c)

$1.08^{\frac{1}{7}}$

d)

$8^{\frac{1}{7}}$

3.

Decreasing 4% each year.

What is the growth factor each month?

a)

$\frac{4\%}{12\ months}$

b)

$\frac{1.04}{12\ months}$

c)

$1.04^{\frac{1}{12}}$

d)

$0.96^{\frac{1}{12}}$

4.

A population doubles every 6 hours. By what factor does it grow each hour?

a)

$\sqrt[6]{2}$

b)

$\sqrt{6}$

c)

$\sqrt{\frac{2}{6}}$

d)

$\sqrt{\frac{6}{2}}$

5.

A population triples every 8 hours. By what factor does it grow each hour?

a)

$\sqrt[8]{3}$

b)

$\sqrt[3]{8}$

c)

$\sqrt{\frac{3}{8}}$

d)

$\sqrt{\frac{8}{3}}$

6.

A bacteria population is tripling every hour. By what factor does the population change in a 1/2 hour?

Select all that apply.

a)

$\sqrt{3}$

b)

$\frac{3}{2}$

c)

$\sqrt[3]{2}$

d)

$3^{\frac{1}{2}}$

e)

$3^2$

7.

At 7a.m., a colony of 100 bacteria is placed on a petri dish where the population will triple every 6 hours.

Select ALL statements that are true.

a)

When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.

b)

Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.

c)

In the first hour the colony is placed on the petri dish, the population grows by a factor of 3^1/6

d)

Between 8a.m. and 9 a.m., the population grows by a factor of 3^2/3

8.

In a pond, the area that is covered by algae doubles each week. When the algae was first spotted, the area it covered was about 15 square meters.

Which expression represents the area covered by algae 1 day after it was spotted.

a)

$15\ \cdot\ ^7\sqrt{2}$

b)

$15\ \cdot\ 2^1$

c)

$15\ \cdot\ 2^7$

d)

$15\ \cdot\ 2\ \left(\frac{1}{7}\right)$

e)

$15\ \cdot\frac{2}{7}$

9.

Caffeine has an average half-life of about 5 hours. A man consumes an energy drink that contains 72 mg of caffeine. Which function represents the amount of caffeine left after h hours?

a)

$72\cdot\left(\frac{1}{2}\right)^{5h}$

b)

$72\cdot\left(\frac{1}{2}\right)^h$

c)

$72\cdot\left(\frac{1}{2}\right)^{\frac{h}{5}}$

d)

$f\left(h\right)=72\cdot\left(\frac{1}{2}\right)^{\sqrt{h}}$

e)

$72\cdot\frac{1}{5}\cdot\left(\frac{1}{2}\right)^h$

10.

The value of a truck decreases exponentially since its purchase. The two points on the graph shows the truck’s initial value and its value one decade afterward.

Write an expression to represent the truck's value 3 years after purchase.

a)

$\ 40,000\ \cdot\ \left(0.85\right)^3$

b)

$\ 40,000\ \cdot\ \left(0.75\right)^{\frac{3}{10}}$

c)

$\ 40,000\ \cdot\ \left(0.85\right)^{\frac{3}{10}}$

d)

$\ 40,000\ \cdot\ \left(0.75\right)^3$

e)

$\ 40,000\ \cdot\frac{1}{10}\left(0.85\right)^3$

11.

A population is growing exponentially by a factor of 1.15 every 3 months. Select ALL the expressions that represent the monthly growth factor.

a)

$\frac{1.15}{3}$

b)

$3^{1.15}$

c)

$\sqrt{3}$

d)

$\left(1.15\right)^{\frac{1}{3}}$

e)

$^3\sqrt{1.15}$

12.

The graph shows a vehicle's value when it is first purchased and it's value 2 years later.

What expression represents the value of the vehicle t years after purchase.

a)

$27850\ \sqrt{1.205\ ^t}$

b)

$27850\ \sqrt{0.83\ ^t}$

c)

$27850\ \frac{0.83^{\ t}}{2}$

d)

$27850\ \frac{1.205^{\ t}}{2}$

13.

The coordinates of Q are (0, 35) and R are (1.5, 14). Which function represents the graph.

a)

$\ 35\cdot\ \left(2.5\right)^{1.5x}$

b)

$35\cdot\ \sqrt[1.5]{0.4}^x$

c)

$\ 35\ \cdot\ \left(\frac{0.4}{1.5}\right)^x$

d)

$35\cdot\ ^3\sqrt{0.4}\ ^x$

e)

$\ 35\ \cdot\ \left(\frac{2.5}{1.5}\right)^x$

14.

A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon.

Which equation represents the amount of medication left after h hours?

a)

$f\left(h\right)\ =\ 225\cdot\left(0.5\right)^{\frac{h}{4}}$

b)

$f\left(h\right)\ =\ 225\cdot\left(-0.5\right)^h$

c)

$f\left(h\right)\ =\ 225\cdot\left(4\ \frac{1}{2}\right)^h$

d)

$f\left(h\right)\ =\ 225\cdot\left(\frac{0.5}{4}\right)^h$

e)

$f\left(h\right)\ =\ 225\cdot\sqrt{0.5}^{4h}$

15.

At the beginning of the year a blogger had 200 subscribers. Since then, the number of subscribers has been doubling every 8 weeks.

Select ALL equations that represent the number of subscribers, S, in terms of w weeks since the beginning.

a)

$S\ =\ 200\cdot w^2$

b)

$S\ =\ 200\cdot2^{\frac{w}{8}}$

c)

$S\ =\ 200\ \cdot\left(\frac{2}{8}\right)^w$

d)

$S\ =\ 200\cdot\sqrt[8]{2}^w$

e)

$S\ =\ 200\cdot8^w$

16.

The function represents a population increasing exponentially in y years.

Which function correctly shows the population in m months?

a)

$p\left(m\right)\ =\ 40\left(1.07\right)^{\frac{m}{12}}$

b)

$p\left(m\right)\ =40\left(1.07\right)^{12m}$

c)

$p\left(m\right)\ =40\left(\frac{1.07}{12}\right)^m$

17.

The function represents a population decreasing exponentially in w weeks.

Which function correctly shows the population in d days?

a)

$f\left(d\right)\ =78\left(0.92\right)^{\frac{d}{7}}$

b)

$f\left(d\right)\ =\ 78\left(0.92\right)^{7d}$

c)

$f\left(d\right)\ =\ 78\left(\frac{0.92}{7}\right)^d$

18.

The table shows the amount of caffeine in a person's system decreasing exponentially. Write an equation for m(h), where m is the amount of caffeine and h is the time in hours.

a)

$m\left(h\right)\ =\ 200\left(0.78\right)^{\frac{h}{2}}$

b)

$m\left(h\right)\ =\ 200\left(0.78\right)^h$

c)

$m\left(h\right)\ =\ 200\left(0.78\right)^{\frac{h}{24}}$

19.

The graph shows a function decreasing exponentially. Write an equation for the function.

a)

$f\left(x\right)\ =\ 220\cdot\sqrt[7]{0.83}$

b)

$f\left(x\right)\ =\ 220\cdot\sqrt[2]{0.83}$

c)

$f\left(x\right)\ =\ 220\cdot\left(0.83\right)^x$

20.

The table shows a population increasing exponentially. Write an equation for p(y).

a)

$p\left(y\right)\ =\ 40\left(1.08\right)^{\frac{y}{2.5}}$

b)

$p\left(y\right)\ =\ 40\left(1.08\right)^y$

c)

$p\left(y\right)\ =\ 40\left(1.08\right)^{\frac{y}{2}}$

Unit 4a Remediation - Standard #1 Recognize Situations

Total questions: 20

Worksheet time: 11mins

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