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Exponential Equation: f(x) = bx
What does the "b" stand for?
What does the "x" represent?
b = base
x = exponent
A = P(1 + r)t
P =
r =
t =
P = Initial amount
r = rate
t = time
Rewrite log381 = 4 as an exponential equation.
34 = 81
Solve. 3x + 1 = 13
x = 1.3347
f(x) = (7/9)x - 4
Does this function represent growth or decay?
Decay
A population of 12 million will double in 35 years. What will the population be 20 years from now?
P = P0(2t/d)
In this scenario, what is P0, t, d
P0 = 12 million
t = 20
d = 35
Using the change of base formula, rewrite log1229
log29/log12
or
ln29/ln12
Solve. ln(5x - 4) = 9
x = 1621.4168
f(x) = 4x - 1
Complete a table of of points for a graph where x = -2, -1, 0, 1, 2
(-2, -15/16), (-1, -3/4), (0, 0), (1, 3), (2, 15)
You are going to invest $2000. You plan to leave the money in the account for the next 10 years. Calculate the account's outcome if it earns 3% interest compounded monthly.
$2698.71
State the domain, range, and asymptote for f(x) = log4(x - 2)
Domain = (2, + infinity)
Range = (- infinity, + infinity)
Asymptote: x = 2
Solve. 5(2x) + 7 = 11
x = -0.3219
f(x) = -(2)(x + 2) - 5
Name all transformations of this function.
Aluminum-26 has a half life of 740,000 years. In 2012, a recycle center had 235,000 pounds of aluminum. How much aluminum would we expect to be remaining in 2092?
234,982.391 pounds of aluminum
Condense: 2log4x + log4y
log4(x2y)
Solve. log(x - 1) + log(x) = log(2)
x = 2
1/81 = 9-3x
Solve for x
x = 2/3
You are going to invest $2200 but need to decide what investment to put it in. You plan to leave the money in the account for the next 5 years. Calculate each account's outcome and determine which account you would invest your money in.
Earns 2% interest compounded semi-annually
Earns 1.8% interest compounded continuously
2% compounded semi-annually = $2430.17
1.8% compounded continuously = $2407.18
First option is better.
Expand: log2(z6/x4y3)
6log2z - 4log2x - 3log2y
Solve. e2x - 4ex - 5 = 0
x = 1.61