Word Problems
A new car is purchased for 23200 dollars. The value of the car depreciates at 13.25% per year. What will the value of the car be, to the nearest cent, after 7 years?
y≈8577.77
log3(27) = 3
33 = 27
log a - 2log c
log (a/c2)
log2√2
1/2
f(x) = 2log3(x-1)
What is the domain, range, end behaviors, and asymptote?
Domain: increasing (1, ∞)
Range: (-∞, ∞)
End behaviors: left - x → 1 (from the right), y → -∞ and right - x → ∞, y → ∞
Asymptote: x=1
A culture of bacteria has an initial population of 1500 bacteria and doubles every 2 hours. Using the formula Pt=P0⋅2(t/d), where Pt is the population after t hours, P0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?
Pt = 16970.5627 ≈ 16971
3-4 = 1/81
log3(1/81) = -4
log q + ylog r
log(qry)
logx(16) = 2
x = 4
f(x)=−log3x+1
What is the domain, range, end behavior, and asymptote?
vertical asymptote of x = 0. The range of the function is (-∞, ∞), and it is decreasing on its domain of (0, ∞). The end behavior on the LEFT side is as x → 0 (from the right), y → ∞, and the end behavior on the RIGHT side is as x → ∞, y → -∞.
Michael is going to invest in an account paying an interest rate of 6.7% compounded continuously. How much would Michael need to invest, to the nearest dollar, for the value of the account to reach $100,000 in 14 years?
P ≈ 39141
log6(√6) = 1/2
61/2 = √6
4log r - log x
log (r4/x)
Solve the following problem for the positive solution for x.
log3x = -2
x = 1/9 or 3-2
f(x) = -2log3x + 2
What is the domain, range, end behaviors, and asymptote?
The function f(x) is a logarithmic function with a vertical asymptote of x = 0. The range of the function is (-∞, ∞), and it is decreasing on its domain of (0, ∞). The end behavior on the LEFT side is as x → 0 (from the right), y → ∞, and the end behavior on the RIGHT side is as x → ∞, y → -∞.
Tallulah invested $75,000 in an account paying an interest rate of 7 5/8% compounded quarterly. Magan invested $75,000 in an account paying an interest rate of 7 7/8% compounded continuously. After 15 years, how much more money would Magan have in his account than Tallulah, to the nearest dollar?
$11515
log8(√512) = 3/2
83/2 = √512
logxy4
log x + 4log y
228 ⋅ 2x/4 = 96
x ≈ -6.34
f(x) = -2(1/3)x
What is the domain, range, end behaviors, and asymptote?
The function f(x) is an exponential function with a horizontal asymptote of y = 0. The range of the function is (-∞, 0), and it is increasing on its domain of (-∞, ∞). The end behavior on the LEFT side is as x → -∞, y → -∞, and the end behavior on the RIGHT side is as x → ∞, y → 0.
$370 is invested in an account earning 7.5% interest (APR), compounded continuously. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
f(t) = 370(1.0779)t
7.79% increase per year
51/2 = √5
log5(√5) = 1/2
log x3y5
3log x + 5log y
log7(2x) + log7(2) = 5
x = 16807/4
f(x) = -2(2)x + 4
What is the domain, range, end behaviors, and asymptote?
The function f(x) is an exponential function with a horizontal asymptote of y = 4. The range of the function is (-∞, 4), and it is decreasing on its domain of (-∞, ∞). The end behavior on the LEFT side is as x → -∞, y → 4, and the end behavior on the RIGHT side is as x → ∞, y → -∞.