You invest $500 in the stock of a company. The value of the stock decreases 2% each year. Describe and correct the error in writing a model for the value of the stock after t years.

The model should be $$V(t) = 500 * (0.98)^t$$

The model should be $$V(t) = 500 * (1.02)^t$$

The model should be $$V(t) = 500 * (0.02)^t$$

The model should be $$V(t) = 500 * (2)^t$$

Do $$f(x) = 5(4)^{-x}$$ and $$g(x) = 5(0.25)^x$$ represent the same function? Justify your answer.

Yes, they represent the same function because $$4^{-x} = (0.25)^x$$ .

No, they do not represent the same function because $$4^{-x} \neq (0.25)^x$$ .

Yes, they represent the same function because $$4^{-x} = 4^x$$ .

No, they do not represent the same function because $$4^{-x} = 4^x$$ .

When a person takes a dosage of I milligrams of ibuprofen, the amount A (in milligrams) of medication remaining in the person's bloodstream after t hours can be modeled by the equation $$A = I(0.71)^t$$ . Find the amount of ibuprofen remaining in a person's bloodstream for the given dosage and elapsed time since the medication was taken. a. Dosage: 200 mg, Time: 1.5 hours b. Dosage: 325 mg, Time: 3.5 hours c. Dosage: 400 mg, Time: 5 hours

a. 200 mg, b. 325 mg, c. 400 mg

a. 100 mg, b. 150 mg, c. 200 mg

a. 150 mg, b. 200 mg, c. 250 mg

a. 200 mg, b. 250 mg, c. 300 mg

The table shows the amount d that a boat depreciates during each year t since it was new. Show that the ratio of depreciation amounts for consecutive years is constant. Then write an equation that gives d as a function of t. Year, t: 1, 2, 3, 4, 5 Depreciation, d: $$1906, $$ 1832, $$1762, $$ 1692, $1627

Is the ratio of depreciation amounts for consecutive years constant?

What is the equation that gives d as a function of t?

7.2 Exercises Graph Exponential Decay Functions

7.2 Exercises - Graph Exponential Decay Functions

Authored by Yasin Giray

Mathematics

10th Grade

CCSS covered

Used 1+ times

7.2 Exercises - Graph Exponential Decay Functions

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23 questions

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OPEN ENDED QUESTION

3 mins • 1 pt

In the exponential decay model y = $1250(0.85)^t$ , identify the initial amount, the decay factor, and the percent decrease.

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Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Explain how to tell whether the function $y = b^x$ represents exponential growth or exponential decay.

If b > 1, it represents exponential growth; if 0 < b < 1, it represents exponential decay.

If b < 1, it represents exponential growth; if b > 1, it represents exponential decay.

If b = 1, it represents exponential growth; if b = 0, it represents exponential decay.

If b > 0, it represents exponential growth; if b < 0, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tell whether the function f(x) = $3(\frac{3}{4})^x$ represents exponential growth or exponential decay.

Exponential Growth

Exponential Decay

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tell whether the function $f(x) = 4(5/2)^x$ represents exponential growth or exponential decay.

Exponential Growth

Exponential Decay

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tell whether the function f(x) = $(2/7) * 4^x$ represents exponential growth or exponential decay.

Exponential Growth

Exponential Decay

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tell whether the function $f(x) = 25(0.25)^x$ represents exponential growth or exponential decay.

Exponential Growth

Exponential Decay

Tags

CCSS.HSF-IF.C.8B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following graphs represents the function y = $(1/4)(1/3)^x$ ?

A graph that shows exponential decay with a y-intercept at 1/4

A graph that shows exponential growth with a y-intercept at 1/4

A linear graph with a positive slope

A linear graph with a negative slope

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following graphs represents the function y = $(1/3)^x$ ?

A graph that shows exponential decay with a horizontal asymptote at y=0

A graph that shows exponential growth with a horizontal asymptote at y=0

A linear graph with a positive slope

A linear graph with a negative slope

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Graph the function f(x) = $2(\frac{1}{5})^x$ .

The graph is a straight line.

The graph is a parabola.

The graph is an exponential decay curve.

The graph is an exponential growth curve.

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Graph the function y = $-(0.2)^x$ .

The graph is a straight line.

The graph is an upward sloping curve.

The graph is a downward sloping curve.

The graph is a horizontal line.

Tags

CCSS.HSF-IF.C.7E

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7.2 Exercises - Graph Exponential Decay Functions

In the exponential decay model y = 1250(0.85)t1250(0.85)^t1250(0.85)t , identify the initial amount, the decay factor, and the percent decrease.

Explain how to tell whether the function y=bxy = b^xy=bx represents exponential growth or exponential decay.

Tell whether the function f(x) = 3(34)x3(\frac{3}{4})^x3(43​)x represents exponential growth or exponential decay.

Tell whether the function f(x)=4(5/2)xf(x) = 4(5/2)^xf(x)=4(5/2)x represents exponential growth or exponential decay.

Tell whether the function f(x) = (2/7)∗4x(2/7) * 4^x(2/7)∗4x represents exponential growth or exponential decay.

Tell whether the function f(x)=25(0.25)xf(x) = 25(0.25)^xf(x)=25(0.25)x represents exponential growth or exponential decay.

Which of the following graphs represents the function y = (1/4)(1/3)x(1/4)(1/3)^x(1/4)(1/3)x ?

Which of the following graphs represents the function y = (1/3)x(1/3)^x(1/3)x ?

Graph the function f(x) = 2(15)x2(\frac{1}{5})^x2(51​)x .

Graph the function y = −(0.2)x-(0.2)^x−(0.2)x .

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In the exponential decay model y = $1250(0.85)^t$ , identify the initial amount, the decay factor, and the percent decrease.

Explain how to tell whether the function $y = b^x$ represents exponential growth or exponential decay.

Tell whether the function f(x) = $3(\frac{3}{4})^x$ represents exponential growth or exponential decay.

Tell whether the function $f(x) = 4(5/2)^x$ represents exponential growth or exponential decay.

Tell whether the function f(x) = $(2/7) * 4^x$ represents exponential growth or exponential decay.

Tell whether the function $f(x) = 25(0.25)^x$ represents exponential growth or exponential decay.

Which of the following graphs represents the function y = $(1/4)(1/3)^x$ ?

Which of the following graphs represents the function y = $(1/3)^x$ ?

Graph the function f(x) = $2(\frac{1}{5})^x$ .

Graph the function y = $-(0.2)^x$ .