Exponential Functions & Equations
What is the y-intercept of the function:
y=2(3/2)x
2
A magazine had 4000 subscribers at the end of the year 2004. The number of subscribers increased by 10% each year as compared with the previous year.
How many subscribers are there at the end of the year 2007 ?
5324
Expand
log(4x)
log(4) + log(x)
If log4x = 3, then what is x?
64
53x-2 = 25
4/3
What is the asymptote of the function:
y = 2(3/2)x
y=0
James purchased a truck for $25,900. The value of the truck decreases by 12% per year. What will be the approximate value 8 years after the purchase?
$9,314.53
If x= r2/s, write an equivalent expression to log(x). (Expand.)
2log(r) - log(s)
What is the solution to the equation:
log2(8) + log2(32) = x
8
Which of the following statements is/are true based on the definition of a logarithm y = logb(x)?
I. x > 0
II. b > 0
III. b not equal to 1
IV. y > 0
I, II, and III only
Which is true about the function y=ex ?
I. It represents exponential growth.
II. It represents exponential decay.
III. It passes through (0,1)
IV. It passes through (1,0)
I and III only
When interest is compounded n times a year, the accumulated amount (A) after t years is given by the formula:
A = P(1 + r/n)nt
where P is the initial principal and r is the annual rate of interest. Approximately how long, to the nearest hundredth, will it take $2,000 to double at an annual interest rate of 5.25% compounded monthly?
13.23 years
Which expression is not equivalent to logb(36)?
A. 6logb(2)
B. logb(9) + logb(4)
C. 2logb(6)
D. logb(72) - logb(2)
A. 6logb(2)
If log(x) = 2 + log(2), then what is x?
200
Given a starting population of 100 bacteria, the formula b = 100(2t) can be used to find the number of bacteria, b, after t periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200?
135 minutes
To shift the graph of y=3x two units to the right, what is the new equation?
y=3x-2
Drew's parents invested $1,500 in an account such that the value of the investment doubles every seven years. The value of the investment, V, is determined by the equation V = 1500(2)t/7, where t represents the number of years since the money was deposited. How many years, to the nearest tenth of a year, will it take the value of the investment to reach $1,000,000?
65.7 years
If ln(M) = 3ln(r) + 2ln(s), then express M in terms of r and s.
r3s2
If log(N) = 2log(x) + log(y), what is N in terms of x and y?
x2y
Kristen invests $5,000 in a bank. The bank pays 6% interest compounded monthly. To the nearest tenth of a year, how long must she leave the money in the bank for it to double?
11.6 years
Solve:
3(27)x = 1
x= 1/9
The Wongs bought a new house three years ago for $92,000. The house is now worth about $113,000. Assuming a steady annual percentage growth rate, approximately what was the yearly rate of appreciation?
7.1%
If log5=a, then express log250 in terms of a.
2a + 1
log5(2x+1) + log5(x) = log5(10)
2
The number of bacteria present in a Petri dish can be modeled by the function N = 50e3t, where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 30,700.
2.14 hours