Exponential Functions
What is the formula for an exponential function?
f(x)= Cax
What is the formula for compound interest?
A= P(1+ r/n)nt
Solve:
log3(1)
log2(2)
log3(1)= 0
log2(2)= 1
What is the Natural Log?
loge(x)= ln(x)
Does this function grow or decay?
g(t)= 4/9 (2/5)t
Decay because 1>a>0
What value does the "C" in the function f(x)= Cax represent?
C= the initial value or the y-intercept
How would you convert 4.2% interest to a decimal?
4.2% turns into .042
*move the decimal two places to the left
Solve:
log25 + log2x - log210
log2(x/2)
What is the base of ln? With this in mind, solve this equation:
ln(e)= ?
ln(e)= 1
What is another way we can write log52?
2log5
The population of HomeTown in 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%. Write an equation that represents this information.
35,000(1+.024)x
How much would you have to deposit in a savings account paying 4.9% annually so that you will have $60,000 in your account after 12 years?
*hint: you are not solving for A
P= $33, 795.20
Expand the log:
log(x2y3)/ (Z4)
2 log(x)+ 3 log(y)- 4 log(z)
Solve for x:
ln ex + ln e5= 1
x= -4
Expand the expression:
logb(b/x)
1- logbx
Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom each day. If you begin with 100 mg of Bismuth-210, how much remains after one week?
100(.87)7= 37.73
If you deposit $4,000 in an account that pays 2.92% interest semi-annually, what is the balance after 5 years?
A= $4623.90
Solve:
log9911- log464
8
Solve for x:
e3x = 9
Solve:
5 log3(9x)= 15
x= 3
Does this function grow or decay:
h(x)= 2.05(3)x
Grow because a>1
Chocolate or vanilla?
7 log3(x)- 4 log3(x)
log3x3
Solve for x:
ln (x) + ln (x+3)= ln (20-5x)
x= 2
*x= -10 is extraneous
Solve:
82x+1= 32
x= .3