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 NFL?
32
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.
Solve the following logarithm for x.
logx625 = 4
x = 5
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
What is the relationship between the horizontal asymptote and the range in regards to an exponential function?
The horizontal asymptote will be the lowest value of the range. The range will approach the horizontal asymptote but never touch it.
What are the two special forms of logarithms and what are their bases?
Common logarithm- base of 10
Natural logarithm- base of e
Solve the following logarithm.
5log3(x+6) = 20
75
What is Baby Yoda's real name?
Grogu
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
Given the equation: 2(1/4)x + 3 Find the following,
Horizontal Asymptote
Domain
Range
HA: y=3
Domain: (-inf, +inf)
Range: (3, +inf)
Calculate the following logarithm using the change of base formula
log872=x
x= 2.06
Solve the following logarithm.
log5(x2+x)= log5(12)
Hint: Factor
x = -4, 3
Can you name 10 African countries?
See if student team can guess 10 countries
In 1980 the population of the state of NC was 5.9 million. By 2023 the population of the state of NC was 10.8 million. Assuming the population grows continuously, determine the rate of growth for the population of North Carolina.
Approximately 1.4%
Longleaf School of the Arts has a population of 430 students as of 2023. The school projects the population of the school to grow 1.8% each year. By what year will the school reach 500 students?
2031
What is the key relationship between exponentials and logarithms?
ex. ln(ex) or log(10x)
They are inverses!
Find the numerical value of the log expression
log(a) = 2 log(b) = 4 log(c) = 1
log( a3b4/c2)
20
How many keys are there on a piano?
88