Identify the model represented by: f(X)= (3/4)^x+5
What is exponential decay?
100
Expand: logx^4y/√z
What is 4logx+logy -1/2 logz?
100
Simplify: ln X^2
What is x^2?
100
Find the number of years for $1000 investment to double at 7% interest rate compunded
What is t= ln2/.07 = 9.9?
100
9-3/2
What is 1/27?
200
Identify the model represtned by: f(x) = 1/2+3e^(2X)
What is logistic growth?
200
Use the change of base formula to solve the log: log base 7 of 3
What is log base 10 of 3/ log base 10 of 7 = .5646?
200
Solve for x: log base 4 of x=3
What is x=64?
200
Determine the amount of money that should be invested at a rate of 6% compounded annually to produce a final balance of $2000 in 5 years
What is $1,494.52?
200
3a-2(2b)3
What is 24b3/a2?
300
Identify the model represnted by: f(X)= 1/2e^(.0567x)
What is exponential growth?
300
Write as a single quantity: [2logx+5logy]-1/3logz
What is logx^2y^5/cube root of z?
300
Solve: 7-2e^x=4
What is x=ln(3/2)= .4055?
300
An initial deposit of $2000 is made in a savings account for which the interest is compounded continuously. The balance will triple in 20 years. What is the annual rate of interest
What is r= ln3/20 = 0.05?
300
Log 16 4
What is 1/2?
400
In 1985, you brought a sculpture for $380. Each year, t, the value, v, of the sculpture increases by 8%. Write an exponential model that describes this situation?
What is v=380(1.08)t?
400
Wite as a single expression: 1/2[ln(x+1)+2ln(x-1)] +3lnx
What is ln[x^3(x-1)√x+1]?
400
Solve: ln(x+1)^2=2
What is x= e-1 = 1.71828?
400
The number of bacteria N in a culture is given by the model below where t is the time in hours. If N=280 when t=10, estimate the time required for the population to double in size. N=250e^kt
What is 61.16 hours?
400
log 243
What is 2.3856?
500
Record albums increased in popularity until 1980. In 1980, 817 (million) record albums were sold. Each year after that, the number sold decreased by 27&. Write an exponential model which describes this.
What is y=817(0.73)x
500
Expand: √x^2(x+2)
What is log(x)+1/2log(x+2)?
500
solve for x: ln(7-x) + ln(3x+5) = ln(24x)
What is x=7/3?
500
The population P of a city is given by P=2500e^kt where t= 0 represents 1990. In 1945, the population was 1350. Find the value of k