Quiz about Exponential Growth and Decay Word Problems with Half-Life and Doubling Life

Question 1

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

Accepted Answer

25mg

Answer

25g

Answer

10g

Answer

10mg

Question 2

Write and exponential function for the following problem: Mrs. Madison starts the year off with 100 pencils. Each week, half of the pencils disappear. How many would be left after x weeks?

Accepted Answer

$$y=100\left(\frac{1}{2}\right)^x$$

Answer

$$y=100\left(2\right)^x$$

Answer

$$y=2x\ +\ 100$$

Answer

$$y=\left(\frac{1}{2}\right)^x$$

Question 3

Write an equation for this problem: A population of 1200 bacteria is doubling each day for x days.

Accepted Answer

$$y=1200\left(2\right)^x$$

Answer

$$y=1200\left(\frac{1}{2}\right)^x$$

Answer

$$y=2^x$$

Answer

$$y=2x\ +\ 1200$$

Question 4

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

Accepted Answer

19 to 20 hours

Answer

10 to 20 hours

Answer

15 to 16 hours

Answer

5 to 6 hours

Question 5

Is this exponential growth or decay?

Accepted Answer

Growth because of 1.2

Answer

Growth, because of 7

Answer

Decay, because of 1.2

Answer

Decay because of 7

Question 6

What type of function does the equation y = 2^xrepresent?

Accepted Answer

Exponential Growth

Answer

Exponential Decay

Answer

Linear

Answer

Exponential Decay

Question 7

Is this exponential growth or decay?

Accepted Answer

Decay

Answer

Growth

Question 8

A sailboat that costs $5,950 decreases in value by a decay factor of .89 per year. How much will the boat be worth after 6 years?

Accepted Answer

$2,957.04

Answer

$0.01

Answer

$5,178.97

Answer

$2,992.96

Question 9

Due to its weakening steel industry, Canalave Town has been experiencing a population decline of 10% every year. The current population is 74,000 people. Assuming the trend continues, which equation projects the population in x years?

Accepted Answer

y = 74,000 (0.90)^x

Answer

y = 74,000 (0.10)^x

Answer

y = 74,000 (1.10)^x

Answer

y = 74,000 (1.90)^x

Question 10

A city doubles its size every 64 years. If the population is currently 225,000, what will the population be in 128 years?

Accepted Answer

The population will be 900,000.

Answer

The population will be 225,000.

Answer

The population will be 450,000.

Answer

The population will be 1,800,000.

Question 11

You buy a new computer for $2100. The computer decreases by 50% annually. Which function represents the situation?

Accepted Answer

$$y\ =\ 2100\left(1-\frac{50}{100}\right)^t$$

Answer

$$y\ =\ 2100\left(1+\frac{50}{100}\right)^t$$

Answer

$$y\ =\ 50\left(1-\frac{2100}{100}\right)^t$$

Answer

$$y\ =\ 50\left(1+\frac{2100}{100}\right)^t$$

Question 12

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

Accepted Answer

y = 30,010 (1.05)^x

Answer

y = 30,010 (.05)^x

Answer

y = 30,010 (.95)^x

Answer

y = 30,010 (5)^x

Question 13

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

y=5000(0.7)^x

Answer

y=30(5000)^x

Answer

y=5000(1.3)^x

Answer

y=5000xx

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