Algebra

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?

A) 5

B) 25

C) 125

D) 625

3)

If a city that currently has a population of 1000 triples in size every 8 years, what will the population be in 24 years? Is the population growth modeled by a linear function or an exponential function?

A) 12,000; linear

B) 18,000; exponential

C) 20,000; linear

D) 27,000; exponential

4)

Consider this function for cell duplication where the cells duplicate every minute.

f(x) = 75(2)x

Determine what each parameter in the function represents.

A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.

B) The 75 is the initial number of cells, and the 2 indicates that the number of cells increases by 2 every minute.

C) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells doubles every minute.

D) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells increases by 2 every minute.

5)

A certain population of bacteria has an average growth rate of 2% every five hours. The formula for the growth of the bacteria's population is A = P0 · 1.02t.

If you begin with 200 bacteria, about how many bacteria will there be after 100 hours?

A) 220

B) 297

C) 1,449

D) 5,248

6)

What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(x −

3/5)?

A) translate vertically 3/5 units up

B) translate vertically 3/5 units down

C) translate horizontally 3\5 units left

D) translate horizontally 3/5 units right

7)

This exponential function y = 3(2)x + 4 represents the growth of a certain species of animal in a specific area. The y-axis represents the number of that animal present and the x-axis represents years. What can you say about the growth of the population of the species every year?

A) The growth rate doubles each year.

B) The growth rate triples each year.

C) The growth rate increases by 2 each year.

D) The growth rate increases by 5 each year.

8)

Write the explicit formula for the geometric sequence represented by the recursive formula.

a1 = 11

an = 3 · an-1

A) an = 11 · 3^n

B) an = 3 · 11^n

C) an = 11 · 3^n-1

D) an = 3 · 11^n-1

10)

Describe the end behavior of f(x) =

1x/3 - 5. [Note: This is an exponential function where

1/3 is the base and x is the exponent.]

A) As x → -∞, f(x) → -5. As x → ∞, f(x) → ∞.

B) As x → -∞, f(x) → 0. As x → ∞, f(x) → ∞.

C) As x → -∞, f(x) → ∞. As x → ∞, f(x) → -5.

D) As x → -∞, f(x) → ∞. As x → ∞, f(x) → 0.

11)

Simplify the following expression

4x0 y-2 z3/4x

A)

0/4x

B)

z^3/xy^2

C)

4z^3/xy^2

D) -y^2z3

12)

Which equation represents the graph shown?

A) y = 2(x - 1) - 2

B) y = 2(x - 1) + 2

C) y = 2(x + 1) - 2

D) y = 2(x + 1) + 2

13)

Which exponential function/geometric sequence matches the graph?

A) y = -1/2^x

B) y = 1/2^x

C) y = -2x

D) y = 2x

14)

Write an equation that models the sequence 400, 200, 100, 50, ...

A) y = 400(2^x)

B) y = 50 (2^x)

C) y = 1/2x + 400

D) y = 400(1/2)^x-1

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1. A homework dump? Booo! Still, I'll try to get you started on these, just 'cause I'm feeling generous right now.

#1. as x grows by 2, 3*5^x grows by a factor of 5^2
#3. 24 = 8*3, so it triples 3 times, right?
#4. initial value is when x=0. 2^0 = 1...
#5. just plug in t=100
#6. f(x-h) shifts the graph to the right by h
#7. none of the above. That pesky +4 messes up the ratios
#8. well, you keep multiplying by 3 for each successive term. What does this whole set of exercises deal with?
#10. (1/3)^x gets smaller and smaller, since you keep multiplying by a number less than 1. It is like the left side of the graph of 3^x
#11. 4x^0 y^-2 z^3/4x = (4*1*z^3)/(y^2*4x) = ...
#12,13. no idea -- no graph
#14. well, you keep multiplying by 1/2, right?

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posted by oobleck

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