Exponent Rules
Writing Exponential Equations from 2 points
Exponential Word Problems
100
Simplify the expression:
(7x^2)(3x^3)
21x^5
100
Write an exponential function for a graph that passes through the points (2, 16) and (3, 32). Write the function in the form y=a(b)x
y=4(2)x
100
A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function f(x) to model the situation where x is the number of 30-minute time periods.
f(x) = 50(2)x
200
Simplify the expression:
47x^2+3x^2
50x2
200
Write an exponential function for a graph that passes through the points (2, 90) and (4, 810). Write the function in the form y=a(b)x
y=10(3)x
200
Enrollment at a school is initially 446 students and grows by 8% per year.
Write the exponential function for this scenario.
y = 446(1.08)x
300
Simplify the expression (no negative exponents in answer):
(3x^2xy^4)/(6x^5yx^-3)
(y^3x^3)/(2x^2)
300
Write an exponential function for a graph that passes through the points (1, 12) and (3, 192). Write the function in the form y=a(b)x
y=3(4)x
300
Annual Sales for a company are $250,000 and increases at a rate of 9% per year.
Write the exponential function for this scenario.
y = 250000(1.09)x
400
Simplify the expression (no negative exponents in answer):
(7x^2 2x^2y^3)/(6x^5y)
(7y^2)/(3x)
400
Write an exponential function for the graph.
y=-1(3)x
400
A textile company bought a piece of weaving equipment for $60,000. It is expected to depreciate at an average rate of 10% per year.
Write an equation for the value of the piece of equipment Z after t years.
Find the value of the piece of equipment after 6 years. Round the nearest dollar.
Z = 60000(.9)t
Z(6) = 31886
500
Simplify the expression (no negative exponents in the answer)
(2x^2x^6y^-3)/(6x^5y^-1)
x^3/(3y^2)
500
Write an exponential function for the graph.
y=1(1/3)x
500
The population of New York City was 8,192,426 in 2010. The annual rate of population increase for the period was about 0.9%.
Write an equation for the population, P, t years after 2010.
Use the equation to predict the population of New York City in 2025.
P = 8192426(1.009)t
P(15) = 9370872