Basics
Interpreting/Context
Growth vs Decay
Real-World Exponentials
100
What are the a and b values in the exponential equation
y=12(4.5)^x
a = 12
b = 4.5
100
A new influencer started tracking her followers each day and the growth of her TikTok account can be modeled by the equation
g(n) = 10,000(11/10)ⁿ
, what does the 10,000 represent?
She initially had 10,000 followers when she started tracking the growth of her account.
100
An exponential function is given by the equation
y=0.75(1.023)^x
Is this showing growth or decay? And by what percentage is it growing or decaying?
Growing by 2.3%
100
A savings account earns 6% interest annually, compounded monthly. If you put $1200 in and don't touch it, what will the value be after 7 years?
$1824.44
200
A population doubles every year and starts with 42,500 people. Write an equation for the population, p, after n years.
p=42500(2)^n
200
The population of microorganisms in a petri dish is a function, f, of the number of weeks, w, since
the cultivation began. The equation below represents the population. What is f(-3) and what does it mean in context of this problem?
f(w)=2000(6/5)^w
f(-2)=1157.41
There were 1157.41 microorganisms in the petri dish 3 weeks before the cultivation began.
200
A new Toyota 4 Runner costs $46,985 and loses
1/5
of its value each year. Write an equation to calculate the value of the car, v, after t years.
v=46985(4/5)^t
200
In 1990, the number of patients for one specialist was 435. Each year, the number of patients decreased by 20%.
y=435(0.8)^x
300
Write the equation for the exponential function from this table of values:
y=8(3)^x
300
The function
c(x) = 72(1.04)^x
models the cost in dollars, c, of the average family grocery bill where x represents the number of years since 2010.
For what value of x will the grocery bills exceed $90 and what does that mean in context of this question?
f(6) = $91 which means the average grocery bills will cost more than $90 in 2016.
300
Fill in the blanks for the following statements:
For exponential growth, the _____ the b value, the steeper the graph.
For exponential decay, the _____ the b value, the steeper the graph.
Growth = larger b value steeper graph
Decay = smaller b value steeper graph
300
If you need to borrow $4000 from a bank that offers 4.9% annual interest compounded quarterly, how much money will you owe after 5 years if you make no more payments and don't borrow any more?
$5102.88