Quiz about Unit 4 Quiz Practice Exponential

Question 1

Select TWO functions that represent exponential decay

Accepted Answer

$$f\left(x\right)=0.2^x$$

Accepted Answer

$$f\left(x\right)=\left(\frac{1}{6}\right)^x$$

Answer

$$f\left(x\right)=1.2^{2-x}$$

Answer

$$f\left(x\right)=\left(\frac{7}{6}\right)^x-2$$

Question 2

The equation $$f\left(t\right)=540,000\cdot\left(1.05\right)^t$$

represents the value of a house, in dollars, t years after it was purchased. What was the purchase price of the house?

Accepted Answer

$540,000

Answer

$105,000

Answer

$567.000

Answer

$640,000

Question 3

A lake is 10 miles long, Its length is decreasing by 3% every 13 years. if f(x) is the lake's length in miles after x years, which function describes the situation?

Accepted Answer

$$f\left(x\right)=10\left(0.97\right)^{\frac{x}{13}}$$

Answer

$$f\left(x\right)=10\left(0.03\right)^{-13x}$$

Answer

$$f\left(x\right)=10\left(0.03\right)^{-\frac{x}{13}}$$

Answer

$$f\left(x\right)=10\left(0.97\right)^{13x}$$

Question 4

Which of the follow represents a decreasing function?

Accepted Answer

Question 5

A sample of bacteria has a weight of 26 mg and a half-life of 7 days. How much of the bacteria will remain after 1 week?

Accepted Answer

13 mg

Answer

26 mg

Answer

3.7 mg

Answer

6.5 mg

Question 6

This model shows the value of a home where t is the number of years since the house was purchsed

$$f\left(t\right)=135,000\left(1.08\right)^t$$

How many years will it take for the value of the home to be over $200,000

Accepted Answer

6 Years

Answer

5 Years

Answer

4 Years

Answer

2 Years

Question 7

In 2020 the cost of a car was $45,000. Since then, its value has depreciated 6% per year. Which equation represents the value of the car as a function of time (t) in years since 2020?

Accepted Answer

$$f\left(t\right)=45,000\left(.94\right)^t$$

Answer

$$f\left(t\right)=45,000\left(.06\right)^t$$

Answer

$$f\left(t\right)=45,000\left(1.06\right)^t$$

Answer

$$f\left(t\right)=45,000\left(1.94\right)^t$$

Question 8

Which of the following has the most rapid rate of change?

Accepted Answer

$$y=5\left(5^x\right)$$

Answer

$$y=5\left(2^x\right)$$

Answer

$$y=2\left(5^x\right)$$

Answer

$$y=2\left(2^x\right)$$

Question 9

A bacteria population is growing exponentially with a growth factor of 6 each day. By what growth factor does the population change each hour?

Accepted Answer

$$6^{\frac{1}{24}}$$

Answer

$$\left(\frac{1}{6}\right)^{24}$$

Answer

$$6$$

Answer

$$24^{\frac{1}{6}}$$

Question 10

The population of a city in thousands is modeled by the function $$f\left(t\right)=250\cdot\left(1.01\right)^t$$ where t is the number of years after 1950. Which of the following are predicted by the model? Select all that apply.

Accepted Answer

The population in 1950 was 250,000

Accepted Answer

The population in 1951 was 252,500

Answer

The population in 1950 was 250

Answer

The population grows by 10 percent each year

Answer

The population DOES NOT grow exponentially

Question 11

Mrs. Wilson drinks coffee every morning with 100 mg of caffeine. Half of the caffeine is in her body 3 hours later. Which function f could describe the caffeine h hours after drinking her coffee, assuming it decays exponentially?

Accepted Answer

$$f\left(t\right)=100\left(\frac{1}{2}\right)^{\frac{h}{3}}$$

Answer

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

Answer

$$f\left(t\right)=100\left(2\right)^{\frac{h}{3}}$$

Answer

$$f\left(t\right)=100\left(\frac{1}{2}\right)^{3h}$$

Question 12

The tuition at a college has been increasing 3% every year and is given by the following function

$$f\left(t\right)=25,000\cdot\left(1.03\right)^t$$

What will the tuition be in 7 years?

Accepted Answer

$30,747

Answer

$5747

Answer

$26,750

Answer

$30,626

Question 13

By what factor (b) did the population grow in the first hour?

Accepted Answer

$$\frac{4}{3}$$

Answer

$$\frac{3}{4}$$

Answer

$$1$$

Answer

not enough information given

Question 14

Which equation represents the bacteria population, b,

and the number of hours since it was measured, h.

Accepted Answer

$$b\left(h\right)=30\left(\frac{4}{3}\right)^h$$

Answer

$$b\left(h\right)=40\left(\frac{4}{3}\right)^h$$

Answer

$$b\left(h\right)=30\left(\frac{3}{4}\right)^h$$

Answer

$$b\left(h\right)=40\left(\frac{3}{4}\right)^h$$

Answer

$$b\left(h\right)=30\left(40\right)^h$$

Question 15

Which of the following equations represents a half life?

SELECT ALL THAT APPLY

Accepted Answer

$$f\left(t\right)=23\left(\frac{1}{2}\right)^t$$

Accepted Answer

$$f\left(t\right)=264\left(0.5\right)^t$$

Answer

$$f\left(t\right)=0.5\left(2\right)^t$$

Answer

$$f\left(t\right)=24\left(3\right)^{\frac{t}{2}}$$

Question 16

Which function DOES NOT match the graph?

SELECT ALL THAT APPLY

Accepted Answer

$$f\left(d\right)=20\left(2\right)^{7d}$$

Accepted Answer

$$f\left(w\right)=20\left(\frac{1}{2}\right)^w$$

Accepted Answer

$$f\left(w\right)=40\left(2\right)^w$$

Answer

$$f\left(w\right)=20\left(2\right)^w$$

Answer

$$f\left(d\right)=20\left(2\right)^{\frac{d}{7}}$$

Unit 4 Quiz Practice Exponential

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