Exponential Functions (Graphing/Solving)
Write an equation for the parent function f(x)=2x that has been reflected, shifted left 5, and down 8.
f(x)=-2x+5 - 8
log4 -3v = log4 (-5v-10)
v = -5
Convert to exponential form
log1215 = x
12x=15
Expand
ln (a3/b)2
6 ln a - 2 ln b
classify the equation as exp growth or exp decay
-1/2 * 4x-6
exp decay
Write an equation for the parent function f(x)=2x that has been compressed by 3, shifted right 5, and up 4.
f(x) = 3*2x-5 + 4
log5 7 + log5 2x = 1
x = 5/14
Convert to logarithm form
17x=59
log759 = x
condense
36 ln x + 6 ln y
ln (x36y6)
A baseball card that was valued at $200 in 1980 has increased in value by 7% each year. Find the value of the card in 2016.
$2284.79
Solve the exponential equation:
5-3a + 1 = 5-2a
a = 1
Solve
2 * log x - log 4 = 2
x = -20, 20
Condense
2*log6 x - 5*log6 y
log6 x2/y5
Solve
ln 72 - ln 4 = ln 6 + ln (a-2)
a = 5
Jack bought a new car in 2014 for $28,000. If the value of the car decreases by 14% each year, estimate how much the car will be worth in 2024.
$6196.44
Solve the exponential equation:
4-b * 4-3b = 42
b = -1/2
Solve
6b-9 + 8 = 30
10.73
Expand
log8 (7*116)5
5*log8 7 + 30*log8 11
Solve
ln 8x = 2
x = .92
Michelle invested $10,000 in an account that earns 8.5% interest that is compounded quarterly. Determine the amount of money in the account in 15 years.
$35,312.15
Solve the exponential equation:
4 * 643n = 1/64
n = -4/9
Solve
14x+6 + 10 = 63
-4.50
Condense
log6 3 + log6 10 + 6*log6 7
log6 3,529,470
Solve
2ec-9 + 3 = 87
c = 12.74
Sarah moved $30,000 of her savings to a new investment account that earns 4% interest compounded quarterly. Find the amount of interest the account will earn after 12 years.
$48,366.78