Exponential equations
Graphing
Word problems
Log equations
Other
100
8c+1 = 162c+3
c = -9/5
100
Graph the following function and state its domain and range:
f(x) = 3x-3 + 2
100
The population of a city 10 years ago was 150,000. Since then, the population has increased at a steady rate each year. The population is currently 185,000. Write an exponential function that models the population after x years if the population changes at the same rate.
f(x) = 150,000 (1.0212)x
100
log2 (x2 - 7) = log2 (6x)
x = 7 (x = -1 is an extraneous solution)
100
What type of function is used to model the following scenario? "A fossil is believed to have originally contained a certain amount of carbon. Over time, the amount of carbon has been cut by 1/2 about every 5,730 years."
Exponential decay.
200
9x-2 > (1/27)x
x > 4/5
200
Graph the following function and state its domain and range:
f(x) = 2 (3/4)x+1 - 3
200
An equation that models the decline in the number of U.S. farms is y = 3,962,520 (0.98)x, where x is the number of years since 1960 and y is the number of farms. How can you tell this function models a decrease in the number of farms, and what is the percent rate of decrease?
0.98 is the common ratio, and 0 < 0.98 < 1. It is decreasing by 2% per year.
200
log3 (x) + log3 (x-3) = log3 (4)
x = 4
200
What type of function is used to model the following scenario? "Sunny puts savings into a bank account that adds 0.1% interest on the previous balance every month."
Exponential growth
300
4e2x-1 = 5
x = 0.2027
300
What function is represented by the following graph?
*A* y = log(x-5) *B* y = 5 log(x) *C* y = log(x+5) *D* y = -5 log(x)
*C* y = log(x+5)
300
Using y = 3,962,520 (0.98)x, x = years since 1960, predict when the number of farms will be less than 1 million.
Around the year 2028.
300
ln (x+2)2 > 2
x < -4.7183 or x > 0.7183, x =/= 2
300
What type of function is used to model the following scenario? "The world population has been growing for a long time continuously, but will eventually reach its carrying capacity and stop growing."
Logistic growth
400
2a+3 = 32a-1
a = 2.113
400
Bad Korean Joke: What does a clam look like when it smiles?
보조개.
400
You put $7,500 in a savings account paying 3% interest compounded continuously. Assuming no deposits or withdrawals, what is the balance after 5 years?
$8,713.76
400
log4(16) - log4(x) = log4(8)
x = 2
400
Bad Math Joke: What kind of tree does Donghoon climb every day?
Geome-tree.
500
6n-1 < 11n
n < -2.956
500
Bad Math Joke: What happens if you try to grow a tree from a box?
It would have square roots.
500
You put $7,500 into a savings account paying 3% interest compounded continuously. How long will it take for your savings to double?
About 23.1 years.
500
Use log5(11) = 1.4899 and log5(2) = 0.4307 to approximate the value of log5(44).
2.3513
500
Bad Math Joke: How do you make the number seven even?
Remove the "s."