What is the formula for Exponential Functions? How do you know if the function is growing or decaying?
f(x) = Cax
If "a" is greater than 1, the function is growing
If "a" is less than 1, the function is decaying
What is the formula used when compounding interest?
A = P(1 + r/n)nt
Solve:
3b= 17
*Remember, in order to solve a variable trapped in the exponent, you must use LOGS!
2.5789
Expand this Log:
log(3x4y-7)
log(3) + 4log(x) -7log(y)
Solve:
log (5x) = log (2x + 9)
3
Fidel has a rare coin worth $550. Each decade, the coin's value increases by 10%. What expression gives the coin's value, 6 decades from now?
550(1 + 0.1)6
What is the formula used when compounding interest continuously?
A = Pert
Solve:
5 ⋅ 186x = 26
0.0951
Simplify this Log:
2log4(x) + 5log4(y) - 1/2log4(z)
log4(x2y5 / z1/2)
Solve:
−2log5 (7x) = 2
1/35
Find the Exponential Function when given the points:
(1,3) and (2, 4.5)
f(x) = 2(1.5)x
Becky invested $19,800 in a CD that pays an annual interest rate of 5.3%. The CD is set to compound daily. How much is in Becky’s account after 9 years?
$31,901.32
Solve:
16n-7+ 5 = 24
8.062
Expand this Log:
ln(4x3/2y)
ln 4 + 3 ln x - ln 2 - ln y
Solve:
−6log3 (x − 3) = −24
84
Find the Exponential Function when given the points:
(2,2) and (3,4)
f(x) = (1/2)2x
Jake invests in an annuity with an annual fixed interest rate of 6.2%. The annuity compounds monthly. If after 10 years, the account balance is $27,839.45, how much was the beginning investment?
$15,000
Re-write in Logarithmic Form
5 ⋅ 63m = 20
(log64) / 3 = m
Simplify this Log:
ln 5 - 7 ln x4 + 2 ln y
ln (5y2 / x28)
Solve:
log10 (2) + log10 (x) = 1
5
Find the Exponential Function when given the values:
f(-2)= 6.25 and f(2)= .01
f(x)= 1/4(.2)x
A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1,854.00, what will the balance be 5 years from now?
1854e0.03 x 5 ≈ $2,154.04
Where is the best place to eat in Stephenville?
Answers will vary...but Fuzzy's is incorrect
What are your plans for Summer Break?
There is no right answer...but just saying "nothing" is lame.
Solve:
log2 (2x) = log2 (100)
50