Interest
Would the equation (1.032)t represent exponential growth or decay?
Growth
Would 3(7)-x represent exponential growth or decay?
Decay
Convert the following exponential into a logarithm.
45=1024
log41024 = 5
Simplify the following logarithm using the product property of logarithms.
log(3) + log(4)
log(12) or 1.079
How many teams are there in the MLB?
30
What is the basic formula for simple exponential decay?
A(t) = P(1-r)t
Can the base of an exponential be negative? Why or why not?
It cannot be negative, because it would create a discrete graph.
Convert the following logarithm into an exponential
log41024=5
45=1024
Simplify the following logarithm using the quotient property.
Log(24) - log(6)
log(4) or .602
How many stars are there in our solar system?
1 - The sun
Ms. Ohayon bought wanted to invest $5000 into an account gaining 3.5% interest continuously. How much money would she have in that account after 8 years?
$6615.65
For the following rate determine if it is growth or decay, then find the growth or decay factor.
Decrease by 35%
.65 Decay
What are the two special forms of logarithms and what are their bases?
Common logarithm- base of 10
Natural logarithm- base of e
Simplify the following logarithm using the power property
5*log(2)
log(32)
What is Bluey and Bingo's last name
Heeler
Maya has an account that pays 6.7% compounded monthly. How much of an initial investment would she need to reach $25,000 after 15 years?
$9176.73
What is the relationship between the horizontal asymptote and the range in regards to an exponential function?
The range will approach the horizontal asymptote but never touch it. the other end will approach negative or positive infinity, depending on if the graph is reflected or not.
Solve for x.
log872=x
x= 2.06
Simplify the following logarithm using the product property.
log4(6) + log3(7)
Can't be done because they do not have like bases.
Can you name 10 Western European countries?
See if student team can guess 10 countries
In 2023 the population of the state of NC was 10.8 million. Assuming the population grows continuously, and a rate of growth of 1.4% rate of growth for the population of North Carolina. What was the population of North Carolina in 1980?
5.92 Million people
Given the equation: 2(1/4)x + 3 Find the following,
Horizontal Asymptote
Domain
Range
HA: y=3
Domain: (-inf, +inf)
Range: (3, +inf)
What is the key relationship between exponentials and logarithms?
They are inverses!
Challenge Question (Daily Double):
Find the numerical value of the log expression:
Hint (Use your logarithm properties)
log(a) = 4 log(b) = 2
log( a3/b2)
8
How many keys are there on a piano?
88