Sequences
Arithmetic or Geometric? 1, 3, 5, 7, 9 ...
What is the common ratio or difference?
Arithmetic. Common difference = 2
What type of asymptote does an exponential function have? (horizontal or vertical)
horizontal ... but logarithmic functions have vertical
Growth or decay? y = 3(0.5)x
decay
Rewrite in log form: 3x = 92
log392 = x
A student has a baseball card that is worth 85000 VND. He looks up the appreciation rate and finds it to be 2.5% per year. He wants to find out how much it will be worth after 3 years. Write a function B(t) to find the value of the card after t years
B(t) = 85000(1+0.025)t
Write the explicit rule for the sequence: 3, 6, 12, 24, 48, . . .
an = 3(2)n-1
Find the domain of the function
f(x) = log_5(3x - 18) + 4
x > 6 (solve 3x - 18 > 0)
Rewrite in exponential form: log(x - 4) = 5
105 = x - 4
Rewrite in log form: e4x = 17 + y
ln(17 + y) = 4x
A student has a baseball card that is worth 85000 VND. He looks up the appreciation rate and finds it to be 2.5% per year. How much is the card worth after 3 years? Round to the nearest whole number
91536 VND
Write the recursive rule for the sequence: 5, -5, -15, -25, . . .
a1 = 5; an = an-1 - 10
Find the domain and range of the function
f(x) = 3(0.25)^(x - 7) + 3
domain: all real numbers; range: y > 3
Solve for x: 2000(1+x)5 = 2500
x = 0.0456
Rewrite with log rules:
log_5(3x^4)
log53 + 4log5x
A person invests $2560 into an account that earns 5.2% annual interest. Calculate the value of the account after 5 years if the interest is compounded monthly. Round to the nearest cent
$3318.28
Find the sum of the series: 4 + 16 + 64 + 256 + . . . + 16384
21844 . . . use the formula
S_n=(a_1*(1-r^n))/(1-r)
Give one of the reference points for the exponential function
f(x) = 3(2)^(x - 4) + 5
(h, a + k) --> (4, 8)
(1 + h, ab + k) --> (5, 11)
Solve for x: 400e0.014t = 410
1.7638
Rewrite as a single log: 4lnx + 6ln2 - lny
ln((64x^4)/y)
A person invests $2560 into an account that earns 5.2% annual interest. Calculate how long it takes for the investment to reach $4000 if the interest is compounded continuously
8.58 years (8 years and 7 months)