Quiz about Growth Decay and Sequences

Question 1

The first three terms of an a sequence are 3, 11, and 19. Which formula represents the sequence?

Accepted Answer

a_n = 3 + 8(n-1)

Answer

a_n = 8 + 3(n-1)

Answer

a_n = 8(3)^n-1

Answer

a_n = 3 + 8n

Question 2

What is the explicit rule for the sequence? 11, 22, 44, 88...

Accepted Answer

a_n = 11(2)^n-1

Answer

a_n = 2(11)^n-1

Answer

a_n = 11(2)

Question 3

Which explicit formula describes the sequence?

$$-1,\ 3,\ 7,\ 11,\ ...$$

Accepted Answer

$$a_n=-1+\left(n-1\right)\left(4\right)$$

Answer

$$a_n=4+\left(n-1\right)\left(-1\right)$$

Answer

$$a_n=\left(4\right)\left(-1\right)^{n-1}$$

Answer

$$a_n=\left(-1\right)\left(4\right)^{n-1}$$

Question 4

Find a₁₂ in the sequence -1, -3, -9, -27, ...

Accepted Answer

-177,147

Answer

-19,683

Answer

-59,049

Answer

118,098

Question 5

What is the 12th term of the following sequence?

$$\left\{3,-6,\ 12,\ -24,\ 48,\ ...\right\}$$

Accepted Answer

$$-6,411$$

Answer

$$6,411$$

Answer

$$354,294$$

Answer

$$-354,294$$

Question 6

What is the 16th term of the following sequence?

$$\left\{10,\ 12,\ 14,\ 16,\ 18,\ ...\right\}$$

Accepted Answer

40

Answer

36

Answer

38

Answer

42

Question 7

Which of the following exponential functions represents an initial value of 1450 and a decay of 18% for x years?

Accepted Answer

$$y=1450\left(0.82\right)^x$$

Answer

$$y=1450\left(0.18\right)^x$$

Answer

$$y=1450\left(1.18\right)^x$$

Answer

$$y\ =\ 1450\ -\left(0.18\right)^x$$

Question 8

Select all the equations that represent exponential decay.

Accepted Answer

$$y=60\left(0.7\right)^x$$

Accepted Answer

$$y=4\left(\frac{1}{2}\right)^x$$

Accepted Answer

$$y=3\left(0.6\right)^x$$

Answer

$$y=\frac{1}{2}\left(4\right)^x$$

Answer

$$y=80\left(1.4\right)^x$$

Question 9

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

Accepted Answer

y = 15(1.35)^x

Answer

y = 15(35)^x

Answer

y = 15(0.35)^x

Answer

y = 35(1.15)^x

Question 10

A publishing industry report predicts that magazine subscriptions will drop by 10% each year. If this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (Round to the nearest whole number if necessary).

Accepted Answer

34,170

Answer

16,348

Answer

7690

Answer

76,023

Question 11

How do you know that this was exponential growth? $$f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$$

Accepted Answer

Because the 1.3 was bigger than one

Answer

Because the 0.25 was bigger than one

Answer

Because the 0.25 was less than one

Answer

Because the 1.3 was less than one

Question 12

How do you know that this was exponential decay? $$f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$$

Accepted Answer

Because the 0.20 was less than one

Answer

Because the 25 was bigger than one

Answer

Because the 0.20 was bigger than one

Answer

Because the 25 was less than one

Question 13

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

Accepted Answer

f(x) = 417(1.0375)^x

Answer

f(x) = 417(3.75)^x

Answer

f(x) = 417(0.0375)^x

Answer

f(x) = 417(1.375)^x

Question 14

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

Accepted Answer

4%

Answer

104%

Answer

96%

Answer

1.04%

Question 15

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

Accepted Answer

9766

Answer

9765

Answer

9006

Answer

5433

Growth Decay and Sequences

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