Free Printable Unit 4aLesson 6 Practice Problems

1.

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)

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

2.

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)

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

3.

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)

$S\ =\ 200\cdot8^w$

4.

Select ALL equations that represent the revenue, r, as a function of m months.

a)

$r\left(m\right)=\ 72,000\left(1.25\right)^{\frac{m}{3}}$

b)

$r\left(m\right)\ =\ 72,000\cdot\sqrt[3]{1.25}^m$

c)

$r\left(m\right)=\ 72,000\left(1.25\right)^m$

d)

$r\left(m\right)=\ 72,000\left(1.25\right)^{6m}$

e)

$r\left(m\right)=\ 72,000\cdot\sqrt{1.25}^m$

5.

Select ALL equations that represent the weight, w, of a catfish, t weeks since it was first weighed.

a)

$w\left(t\right)\ =\ 0.3\cdot\left(1.25\right)^{\frac{t}{2}}$

b)

$w\left(t\right)\ =\ 0.3\cdot\sqrt{1.25}^t$

c)

$w\left(t\right)\ =\ 0.3\cdot\sqrt[4]{1.25}^t$

d)

$w\left(t\right)\ =\ 0.3\cdot\left(1.25\right)^{\frac{t}{4}}$

6.

The value of a car is decreasing exponentially according to the function V(y).

V\left(y\right)\ =\ 25,800\left(0.73\right)^{\frac{y}{3}}

According to the function, the decay factor 0.73 occurred over how many years?

a)

3

b)

73

c)

25

d)

8

7.

An insect population is rapidly increasing by doubling every 15 days. If there were originally 100 insects, which equation represents the insects after d days?

a)

$f\left(h\right)\ =\ 100\cdot2^{15h}$

b)

$f\left(h\right)\ =\ 100\cdot\ \left(\frac{1}{2}\right)^h$

c)

$f\left(h\right)\ =\ 100\cdot2^{\frac{h}{15}}$

d)

$f\left(h\right)\ =\ 100\cdot30^h$

8.

In 2000 a country had a population of 12.8 thousand. By 2010 the population had increased by 13%. During that decade, the population can be reasonably modeled by an exponential function.

Write an equation to show the country's population p(d), in thousands of people, d decades since 2000.

a)

$p\left(d\right)\ =\ 12.8\left(1.13\right)^d$

b)

$p\left(d\right)\ =\ 12.8\left(0.13\right)^d$

c)

$p\left(d\right)\ =\ 12.8\ +\ 1.3d$

d)

$p\left(d\right)\ =\ 12.8+0.13^d$

9.

In 2000 a country had a population of 12.8 thousand. By 2010 the population had increased by 13%. During that decade, the population can be reasonably modeled by an exponential function.

Select ALL expressions that represent the country's population in 2003.

a)

$p\left(d\right)\ =\ 12.8\left(1.13\right)^{\frac{3}{10}}$

b)

$p\left(d\right)\ =\ 12.8\cdot\sqrt[10]{1.13}^3$

c)

$p\left(d\right)\ =\ 12.8\cdot\sqrt[3]{1.13}^{10}$

d)

$p\left(d\right)\ =\ 12.8\cdot\left(1.13\right)^{2003}$

e)

$p\left(d\right)\ =\ 12.8\cdot\left(1.13\right)^{\frac{1}{3}}$

10.

$y=a\cdot b^x$

Write an equation for the graph in the form:

a)

$y\ =\ 8\cdot\sqrt{2.25}^x$

b)

$y\ =\ 8\cdot2.25^x$

c)

$y\ =\ 8\ \cdot\left(2.25\right)^{\frac{x}{3}}$

d)

$y\ =\ 8\cdot\left(0.44\right)^{\frac{x}{2}}$

11.

$y=a\cdot b^x$

Write an equation that represents the graph in the form

a)

$y=15\cdot\sqrt[4]{1.86}^x$

b)

$y=15\cdot\sqrt[4]{0.54}^x$

c)

$y=15\cdot\sqrt[4]{3.75}^x$

d)

$y=15\cdot\sqrt{1.86}^x$

e)

$y=15\cdot\sqrt{3.75}^x$

12.

Between 1998 and 2018 inflation for prices of goods and services has been about 51%.

If a salon charged $15 for a haircut in 1998, which expression shows what they would've charge in 2005 to keep up with inflation?

a)

$15\left(1.51\right)^{\frac{7}{20}}$

b)

$15\left(1.51\right)^7$

c)

$15\left(1.51\right)^{\frac{1}{2}}$

13.

The value of a house is increasing exponentially. At the beginning of 2015 it was worth $160,000. At the beginning of 2019 it was worth $164,800.

What expression represents the value of the house in 2022?

a)

$160,000\left(1.03\right)^{\frac{7}{4}}$

b)

$160,000\left(1.03\right)^7$

c)

$160,000\left(1.03\right)^{\frac{7}{3}}$

d)

$160,000\left(1.03\right)^{\frac{4}{10}}$

Unit 4aLesson 6 Practice Problems

Total questions: 13

Worksheet time: 7mins

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