Show:
Growth/Decay Rate
Growth/Decay Functions
Compound Interest
Geometric Sequence
Geometric Sequences
100
f(t)=50,000(0.47)^t a) Exponential Decay, 53% b) Exponential Decay, 47% c) Exponential Growth, 47% d) Exponential Growth, 53%
What is A.
100
A chemist observes that there are currently 35 bacteria in a sample he is viewing under a microscope. The culture grows at a rate of 3% every hour. Write an exponential model for the value of the bacteria culture.
What is f(t) = 35(1+.03)^t
100
An account that you opened with $4,500 is compounded monthly at a rate of 3.2%. How much will you have earned after 15 years?
What is f(t)=45,000(1+.032/12)^(12*15) $7267.69 after 15 years
100
Given the following geometric sequence, determine the explicit formula. 162, 54, 18, 6, 2, 2/3
What is 162(1/3)^(n-1)
100
Grace is helping her younger brother clean up his toys. She first picks up only 4 Lego pieces and places them in the toy chest. Grace then selects 8 Lego pieces to put away in the toy chest. The next time, she picks up 16 Lego pieces. Grace continues this pattern until she picks up 128 Lego pieces. a) Write the sequence that models this situation.
What is {4, 8, 16, 32, 64, 128}
200
f(t)=50,000(1.47)^t a) Exponential Decay, 53% b) Exponential Decay, 47% c) Exponential Growth, 47% d) Exponential Growth, 53%
What is C.
200
A chemist observes that there are currently 35 bacteria in a sample he is viewing under a microscope. The culture grows at a rate of 3% every hour. Determine how many bacteria will be in the culture after 6 hours. a) 29 bacteria c) 41 bacteria b) 25, 515 bacteria d) 143,360 bacteria
What is c) 41 bacteria
200
Greer deposits $5000 into an account at BB & T which earns 4.25% compounded semi-annually. Write an exponential model for this situation. Then determine how much Greer after 7 years?
What is f(t)=5000(1+.0425/2)^(2*7) $6711.49
200
Given the following information about the geometric sequence, determine the explicit form and find the 12th term in the sequence. 2, -6, 18, -54, …
What is 2(-3)^(n-1) -354,294
200
Grace is helping her younger brother clean up his toys. She first picks up only 4 Lego pieces and places them in the toy chest. Grace then selects 8 Lego pieces to put away in the toy chest. The next time, she picks up 16 Lego pieces. Grace continues this pattern until she picks up 128 Lego pieces. b) Identify the common ratio of your sequence.
What is r=2
300
f(t)=50,000(1.36)^t
What is Exponential Growth? Rate: 36%
300
As of today, there are 200 unicorns in an enchanted park. The population is decaying at a rate of 3% per year. How many unicorns will live in the enchanted park after 4 years? Show ALL your work to receive full credit.
What is 177 unicorns
300
$25,000 is deposited into an account that is compounded quarterly at a rate of 2.7%. How much money will be in the account after 11 years?
What is f(t) = 25,000(1+.027/4)^(11*4) $33,611.82
300
Given the following information about the geometric sequence, determine the explicit form and find the 12th term in the sequence. a2=24 and a4=216
What is 8(3)^(n-1) a12= 1,417,176
300
Grace is helping her younger brother clean up his toys. She first picks up only 4 Lego pieces and places them in the toy chest. Grace then selects 8 Lego pieces to put away in the toy chest. The next time, she picks up 16 Lego pieces. Grace continues this pattern until she picks up 128 Lego pieces. c) Determine the explicit form for the sequence that models this situation
What is 4(2)^(n-1)
400
f(t)=50,000(.35)^t
What is Exponential Decay? Rate: 65%
400
A pizza making oven costs $16,000 for Papa Johns to purchase. The value of the equipment decreases at a rate of 11% each year. Write an exponential model for the value of the equipment. Then determine the value of the equipment after just 3 years.
What is f(t) = 16,000(1-.11)^t After 3 years: $11,279.50
400
Suppose that $575.75 is invested in a savings account with a growth rate of 12% compounded monthly. What is the future value of the account in 5 years? A) 575.75(1+.12/12)^60 B) 575.75(1.12)^60 C) 575.75(1.12/12)^60 D) 575.75(1.12)^5
What is A.
400
Write the explicit formula for the given sequence. 2, 8, 32, 128
What is f(t) = 2(4)^(n-1)
400
Grace is helping her younger brother clean up his toys. She first picks up only 4 Lego pieces and places them in the toy chest. Grace then selects 8 Lego pieces to put away in the toy chest. The next time, she picks up 16 Lego pieces. Grace continues this pattern until she picks up 128 Lego pieces. d) How many turns will it take for Grace to pick up 128 Lego pieces?
What is 6 turns
500
f(t)=50,000(.98)^t
What is Exponential Decay? Rate: 2%
500
A chemist observes that there are currently 100 bacteria in a sample he is looking at under a microscope. If the culture grows at a rate of 5.3% every hour. Write an exponential model for the value of the bacteria culture.
What is f(t)= 100(1+.053)^t
500
10. You deposit $3500 into an account that earns 10% interest compounded annually. What is the balance after 2 years? A) $700 B) $4200 C) $4235 D) $7000
What is C?
500
Determine the explicit formula for the given sequence. -4, 8, -16, 32
What is -4(-2)^(n-1)
500
Grace is helping her younger brother clean up his toys. She first picks up only 4 Lego pieces and places them in the toy chest. Grace then selects 8 Lego pieces to put away in the toy chest. The next time, she picks up 16 Lego pieces. Grace continues this pattern until she picks up 128 Lego pieces. What is the domain and range for the sequence?
What is Dom: {1, 2, 3, 4, 5, 6} Range: {4, 8, 16, 32, 64, 128}