Writing Exponential Equations
The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years. During the second reunion the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family.
What is f(x) = 154(1.032)^x
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years?
$1751.21
Name and write the equations of the three forms of exponential functions that we have been working with in class.
General Form Exponential Growth/Decay
y=a(1+r)^t
Discreetly Compound Exponential Growth/Decay
y= P(1+ (r/n))^(nt)
Continuously Compounding Exponential Growth/Decay
y=Pe^(rt)
What are the three logarithm rules that we learned in class.
Power Rule
Product Rule
Quotient Rule
The population of wild ducks in LakeCounty is 2,500. The population is decreasing at a rate of 7%a year. Howmany ducks will be left in 10 years?
y=2500(1-.07)^10
The value of a car was $22,000 when it was purchased. They car depreciates at a rate of 19% per year. How much will the car be worth in 8 years?
$4,076.64
Evaluate
ln e
1
Use a logarithm rule to expand this expression AND state which rule you used.
log (x^3)
3 log (x) --> Power Rule
The fish in The Magic Forest Lake were declining at an annual rate of 1.5%. Their current population is estimated at 2500. What would their population be after 10 years?
y = 2500(.985)^10
The population in the town of Deersburgh is presently 42,500. The town has been growing at a continuous rate of 2.7%. What will the population of the town be in 5 years?
48,643 People
What is an asymptote AND why does it exist?
A boundary line the graph approaches, but never touches. Asymptotes exist because they represent mathematical impossibilities. (Where the function is undefined)
Expand the logarithm And state which log rule you used.
log(3*x*y)
log (3)+log (x)+ log (y) -->Product Rule
An initial investment of $100 is now valued at $149.18. The interest rate is 8%, compounded quarterly. How long has the money been invested?
149.18=100(1+(.08/4))^(4*t)
The population of the US in 2005 was 295.5 million and the population of the US in 2023 was 334.9 million. The population grew at continuously. What was the growth rate of the US population during that time span?
0.695% Or r=0.00695
Write out the mathematical expression for the written expression AND evaluate.
"Log base 2 of x equals -3"
x=1/8
Expand the logarithm And state which log rules you used.
log(x^2 / 4)
2 log (x)- log (4)
Write a question that would be modeled by this equation:
4000= 1250e^(-0.042*t)
Answers will vary, but should include:
-continuous
-decreasing
-4.2%
-what is the time?
You invest $4,000 into an account that compounds monthly with an interest rate of 5%. How long will it take for you money to double?
13.89 years
What are the domain and range of the function y=2^x?
Domain: (-infinity, infinity)
Range: (0, infinity)
Use log rules to compress the following logarithmic expression:
3 log(x)+ log (7) - 2 log (y)
log (7x^3/y^2)