Test 4 Review

Growth or Decay

100

What is the growth percentage?

y=2(1.67)^x

67%

200

What is the decay percentage?

y=3(.99)^x

1%

300

y = 9(1.77)^x, represents growth or decay?

Growth

400

y = 9(.57)^x, represents growth or decay?

Decay

500

What is the decay percentage?

y=3(.66)^x

34%

Writing/ Solving Exponential Equations

100

The decay factor of an exponential function P(t) is 0.74. The initial value is 1.5. Find a formula for P(t).

P(t) = 1.5(.74)^t

200

A certain population grows exponentially with a yearly growth rate of 6%. The initial population is 509 individuals.

P(t)=509(1.06)^t

300

Find an exponential model for the data set.

(0, 3.02), (1, 5.13) (2, 8.72), (3, 14.82)

y=3.02(1.70)^x

400

Let y=cx^3.81. If y=15.09 when x=3.25, what is the value of c?

c=.169

500

Solve the exponential equation: 14.16 = 52.65(.75)^x

x = 4.57

Which model is it

100

Determine whether the following data points can be modeled by an exponential function.

(3.17, 10.16), (4.17, 6.10), (5.17, 4.22), (6.17, 2.53)

No, not exponential

200

Determine whether the data points represent a linear, exponential or power (quadratic) function.

(0, -5), (1, 4), (2, 13), (3, 22)

Linear

300

Determine whether the data points represent a linear, exponential or power (quadratic) function.

(1, 10), (2, 20), (3, 40), (4, 80)

Exponential 

400

Determine whether the data points represent a linear, exponential or power (quadratic) function.

(-1, 16), (0, 2), (1, -2), (2, 4), (3, 20), (4, 46)

Power (quadratic)

500

Determine whether the data points represent a quadratic function.

(0, 1), (1, 0), (2, 3), (3, 10), (4, 21), (5, 36), (6, 56)

No - 2nd differences are not the same

Logistic Models

100

An enrollment at a certain university t years after 2000 is modeled by the function:

N = 7161/ (1+3e^-0.61t). The limiting value of the enrollment is:

7161

200

An enrollment at a certain university t years after 2000 is modeled by the function:

N = 7161/ (1+3e^-0.61t). At what enrollment level is enrollment growing at the fastest rate?

3580.5

300

An enrollment at a certain university t years after 2000 is modeled by the function:

N = 7161/ (1+3e^-0.61t). What year was the enrollment growing at the fastest rate?

t = 1.81 so about 2002

400

An enrollment at a certain university t years after 2000 is modeled by the function:

N = 7161/ (1+3e^-0.61t). How many people were enrolled in the year 2000?

1790.25 people

500

What letter in the Logistic Formula represents the limiting value?

K

Quadratics

100

Determine whether the data points represent a quadratic function.

(-2, 12), (-1, 9), (0, 7), (1, 6), (2, 6), (3, 7), (4, 9)

Yes, quadratic

200

The rabbit population on a small island is given by the function

R(t)=130t-.4t²+1050, where t is time in months. When is the maximum population attained?

162.5 months

300

The rabbit population on a small island is given by the function

R(t)=130t-.4t²+1050, where t is time in months. What is the maximum population?

11,612.5 rabbits

400

Find the quadratic regression equation for the data points.

(1, 32.5), (3, 37.3), (5, 36.4), (7, 32.4), (9, 28.5)

y= -.366x²+3.016x+30.42

500

The rabbit population on a small island is given by the function

R(t)=130t-.4t²+1050, where t is time in months. When does the rabbit population disappear from the island?

332.886 months