What do you mean!?
In the function abx, this variable represents the starting value or initial amount
What is a?
The phrase “doubles each hour” means the multiplier is what number?
What is 2?
Which of the following represents exponential growth?
A. y = 5 + 3x
B. y=5(1+0.03)^x
C. y=5(1-0.03)^x
D. y=5x
What is B?
You have 100 grams of a substance that loses 20%.
How much remains after one decrease?
What is 80 grams?
In the formula A=P(1+r/n)^(nt) this letter represents the starting amount or principal.
What is P?
How can you tell if an exponential function represents growth instead of decay?
What is the multiplier is greater than 1?
A value is cut in half each week.
Write the multiplier.
What is 0.5?
A population increases by 12% each year.
What is the growth factor?
What is (1+0.12) or 1.12
A population decreases by 25% each year.
What is the decay factor used in the model?
What is (1-0.75) or 0.75
In A=P(1+r/n)^(nt) , this variable represents the annual interest rate, written as a decimal.
What is r?
When a quantity decreases by the same percent over equal time intervals, what type of model describes the situation?
What is an exponential decay model?
A population starts at 150 and triples each year.
Write the exponential model.
What is 150(3)^t
A town has 800 people and grows by 5% each year.
What are the values of a and r (as a decimal)?
What is a = 800 and r = 0.05?
A town has 500 people, and the population decreases by 8% each year.
What are the values of a and r (as a decimal)?
What is a = 500 and r = 0.08?
In A=P(1+r/n)^(nt) , the variable n tells you this about the interest.
What is the number of times interest is compounded per year?
What type of change happens when a quantity increases by the same percent each time period?
What is exponential growth?
A culture starts with 60 bacteria and doubles every hour.
Write the function.
What is
y = 60(2)^t
An investment starts at $1,000 and grows 7% each year.
Write the exponential growth function.
What is
$1,000(1+0.07)^t
A phone battery starts at 100% and loses 20% each hour.
Write the exponential decay function.
What is 100(1-.20)^t
If you invest $1,000 at 6% annual interest compounded quarterly for 1 year, what is the total amount?
Use
$1,000 × (1 + 0.06/4)^{4×1} = $1,061.363~~$1,061.36
What formula would be used for this:
A substance loses 15% of its mass each hour.
What is a(1-r)^t
A bacteria culture starts with 300 cells and doubles each hour.
How many cells are there after 3 hours?
What is 300(2)^3 =2400
A savings account starts with $400 and grows by 25% each year.
How much is in the account after 2 years? (Nearest cent)
What is
400(1+0.25)^2 = 625.00
A car worth $12,000 depreciates 10% each year.
What is its value after 2 years?
What is $9,720?
You invest $2,000 at 5% interest, compounded monthly for 3 years. What is the total amount?
A=$2000(1+0.05/12)^((12)(3))=$2322.9444~~$2322.94
What is the main difference between these two models?
A(t)=300(1.2)^t
B(t)=300(0.8)^t
What is A represents growth and B represents decay?
A medication starts at 200 mg and becomes half its amount each hour.
How much medication remains after 3 hours?
What is 25 mg?
In the function A(t) = 700(1.15)^t
what percent increase is happening each time period?
What is 15%?
A function is given by A(t)=800(1-0.35) ^t
What does 0.35 represent in context?
What is 35% decrease each time period?
Alex invests $1,200 at 3% interest, compounded monthly, for 5 years. How much money will he have at the end?
A=$1,200(1+0.03/12)^((12)(5))=$1,393.940~~$1, 393.94
A student says the function
P(t)=600(1.03)^t
represents a population that decreases by 3% each year.
Is the student correct? Explain.
What is No, because 1.03 represents a 3% increase, not a decrease?
The function
N(t)=350(2.5)^t
models the number of bacteria in a culture.
Which statement correctly interprets the numbers in the model?
A. The culture starts with 2.5 bacteria
B. The culture grows by 350 bacteria each hour
C. The culture starts with 350 bacteria and multiplies by 2.5 each hour
D. The culture increases by 2.5 bacteria each hour
What is C?
Which investment grows more after 1 year?
Option A: $2,000 at 9% growth
Option B: $2,100 at 8% growth
What is option B?
Option A: $2,000(1+.09)^1 = $2,180
Option B: $2,100(1+0.08)^1 = $2,268
A medicine starts at 500 mg and decreases by 18% each hour.
Which expression represents the amount remaining after 3 hours?
A. 500 ( 0.18 ) ^3
B. 500(1.18)^3
C. 500(0.82)^3
D. 500−0.18(3)
What is C
Which investment earns more after 2 years?
Option A: $1,000 at 8% compounded annually
Option B: $1,000 at 7.5% compounded quarterly
Option A ~~ $1,166.40
Option B ~~ $1,160.22