Solving Exponential Equations
Solve the equation.
5^(x+2)=5^(2x-6)
x=8
Determine if the sequence is arithmetic or geometric and write the explicit formula for the sequence.
53, 40, 27, 14, ...
Arithmetic
a_n=-13n+66
Find the Domain and Range of the function.
f(x)=(1/3)^x
Domain: All Real Numbers
Range:
y>0
Write an equation to represent the scenario.
25 grams of a radioactive material decays at the rate of 7% per year. How many grams are left after t years?
y=25(0.93)^t
Find the first 5 terms of the recursive formula.
a_1=7, a_n=-3a_(n-1)
7, -21, 63, -189, 567
Solve the equation.
3^(2x-9)=27
x = 6
Find the 47th term of the arithmetic sequence where
a_1=-93 and d=18
735
Find the Domain and Range of the function.
f(x)=-(1/3)^x+7
Domain: All Real Numbers
Range:
y<7
Write an equation to represent the scenario.
A company is turning a profit of $40,000 in its first year. Sales have continued to rise by 3.6% per year. If this continues, what will be the profit in t years?
40000(1.036)^t
Find the first 5 terms of the recursive formula.
a_1=25 and a_n=a_(n-1)-7
25, 18, 11, 4, -3
Solve the equation.
7^(2x+10)=1
x = -5
Determine if the sequence is arithmetic or geometric and write the explicit formula for the sequence.
375, 75, 15, 3, ...
Geometric
a_n=375(1/5)^(n-1) ora_n=375(0.2)^(n-1)
Find the Domain and Range of the function.
f(x)=-(1/3)^x-5
Domain: All Real Numbers
Range:
y<-5
You invest $10,000 in a stock that begins to lose value at a rate of 8% per month. How much will the stock be worth in 9 months if it continues at this rate? Round your answer to the nearest dollar.
$4722
Solve the equation.
1/9=27^(x+6)
x=-20/3 or-6 2/3
What is the 10th term of the geometric sequence where
a_1=1/8 and r=2
64
Find the Domain and Range of the function.
f(x)=7(1/3)^x+12
Domain: All Real Numbers
Range:
y>12
Cordova High had 12 feral cats on campus. The population has been increasing by 16.5% per year. If that trend continues, how many cats would there be in 4 years?
22 cats