Free Printable IM Unit 4a

1.

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)

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

2.

The population of a city in thousands is modeled by the function below, where t is the number of years after 2000.

$f\left(t\right)\ =\ 175\ \cdot\ \left(1.04\right)^t$

Which of the following statements are true about the model. Select ALL that apply.

a)

The population in 2000 was 175

b)

The population in 2000 was 175,000

c)

The population grows by 4 percent each year

d)

The population in 1995 was 140,000

3.

A bacteria population is tripling every hour.

By what factor does the population change in a half hour?

a)

$\frac{3}{2}$

b)

$\sqrt{3}$

c)

$\frac{1}{3}$

d)

$\frac{2}{3}$

e)

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

4.

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)

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

5.

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)

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

6.

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)

$^3\sqrt{1.15}$

7.

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)

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

8.

Tuition at a public university was $24,000 in 2005. By 2008 the tuition had increased exponentially by 18%. Since then, it has followed the same trend.

Select all true statements about the growth in tuition.

a)

The tuition cost increased by 6% each year.

b)

The tuition cost roughly doubles in 4 years.

c)

The function

$f\left(x\right)\ =\ 24,000\left(1.18\right)^1$

represents the cost of tuition in 2008.

d)

The expression

$1.18^{\frac{1}{3}}$

represents the annual growth rate.

e)

The function $24,000\left(1.18\right)^{10}$ represents the tuition cost in 2015.

9.

A bank account is growing exponentially. At the beginning of 2010, the balance was $1,000. At the beginning of 2014, the balance was $1,325. What would be the account balance at the beginning of 2019?

a)

$1883.59

b)

$12587.61

c)

$2495.75

d)

$2185.76

10.

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)

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

11.

In 1990, the value of a home was $170,000. Since then, its value has increased 5% per year.

Write an equation to represent the value of the home as a function of time in years since 1990.

a)

$v\left(t\right)\ =\ 170,000\left(1.05\right)^t$

b)

$v\left(t\right)\ =\ 170,000\left(5\right)^t$

c)

$v\left(t\right)\ =\ 170,000\left(1.5\right)^t$

12.

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)

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

13.

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)

$S\ =\ 200\cdot8^w$

14.

The graph shows a wolf population which has been growing exponentially each year. Write an equation relating the wolf population w, and the number of years since it was measured, t.

a)

$w\left(t\right)\ =\ 100\left(1.2\right)^t$

b)

$w\left(t\right)\ =\ 100\left(0.83\right)^t$

c)

$w\left(t\right)\ =\ 100\left(2.2\right)^t$

d)

$w\left(t\right)\ =\ 100\left(1.2\right)^{\frac{t}{4}}$

15.

The graph shows the number of flu cases increasing exponentially. Which function correctly relates the number of flu cases to the number of weeks?

a)

$f\left(w\right)=24\left(1.5\right)^w$

b)

$f\left(w\right)=36\left(1.5\right)^w$

c)

$f\left(w\right)=24\left(0.67\right)^w$

d)

$f\left(w\right)=24\left(1.5\right)^{\frac{w}{5}}$

e)

$f\left(w\right)=24\cdot\sqrt{0.67}^w$

16.

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)

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

17.

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)

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

18.

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)

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

19.

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)

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

20.

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)

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

21.

The value of a car is decreasing exponentially according to the function V(y). This tells us the value has a decay factor of 0.73 over how many days?

a)

5

b)

7

c)

25

d)

73

22.

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)

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

23.

A population is increasing exponentially according to the function P(t). This tells us the population has a growth factor of 1.28 over how many days?

a)

3

b)

7

c)

13,900

d)

28

24.

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)

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

25.

If college tuition is increasing 4% each YEAR, is it increasing 40% in a DECADE?

a)

No, 4% x 4% x 4% .... = 1.04¹⁰

b)

Yes, 4% x 10 years = 40%

26.

If the value is increasing 7% each YEAR, is it increasing 70% in a DECADE?

a)

No, because it's 7% of a DIFFERENT NUMBER each year

b)

Yes, 7% x 10 years = 70%

IM Unit 4a - Algebra 2

Total questions: 26

Worksheet time: 13mins

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