Properties of Exponents
Simplify the Expression. Use only positive exponents. (y3)(y-5)
1/(y2)
A cat population of 200 is increasing at a rate of 20% per month. What equation would represent the cat's population, y, after x amount of months?
y= 200(1.2)x
y = 200(1+0.20)x
Determine whether the table represents growth or decay.
| x | 0 | 1 | 2 | 3 |
| y | 3 | 6 | 12 | 24 |
exponential growth
f(x) = 2x + 1 Evaluate when x = 14
f(x) = 29
What is the common ratio for the sequence 81, 27, 9...
r=1/3
Simplify the Expression. Use only positive exponents. (x4)/(x7)
1/(x3)
The equation y =3000(1.3)x represent the population of some ducks after x years. Identify the initial population of ducks, and the growth rate
Initial population is 3,000.
The growth rate is 30% per year.
A new car cost $25,000 and depreciates at a rate of 20% per year. What function could model the value of the car after x years?
y=25,000(0.80)x
f(x) = -4x - 2 Solve when f(x) = 3
f(x) = -14
What is the explicit formula for the sequence 10, 7, 4...?
an=-3n+13
an = 10 -3(n-1)
Simplify the Expression. Use only positive exponents. (x0y2)3
y6
The initial population of a bacteria is 3,000. It is growing at a rate of 32% per hour. How much bacteria are there after 1 day?
2,359,068 bacteria.
The function y=13,000(0.75)x represents the value of a used car after x years. Identify the initial value of the car and the rate of decay
13,000 is initial value of the car and 25% per year is the decay rate.
f(x) = x^2 + 1 Evaluate when x = 5
f(x) = 26
An auditorium had 30 chairs in the first row, 35 in the second row, 40 in the 3rd row,.... all the way up to the 30th row. How many chairs are in the 25th row?
150 chairs
Simplify the expression...
4a2b5c / 2a4b2c
2b3 / a2
A bank balance of 3000 is compounded monthly at a rate of 4%. What is the equation that models the bank balance?
What is A = 3000(1+0.04/12)12t
From an equation, how can you tell if an exponential function is decaying ?
The common multiplier/ratio is a number between 0 and 1.
g(x) = x^3 - 10. Evaluate when x = 2
g(x) = - 2
Write an equation for the nth term. 1,4,16,64,...
an=4n-1
Simplify the Expression. Use only positive exponents. (2x2/5y4)-2
25y8/4x4
For the last 10 years BoomTown's population has been doubling. Today, its population totals 640,000. How many people lived in GhostTown 10 years ago?
625
A boat cost $15,465 and the value decreases at a rate of 15% per year. How much will the boat be worth after 5 years?
$6861.90.
g(x) = x^2 + 5. Solve for x when g(x) = 14
x = 3
Write an equation for the nth term. 5,-10, 20, -40
an=5(-2)n-1