Condensing/ Expanding
Condense the problem below:
log(3) + log (x)
log (3x)
Solve for X
7x = 9
x= (ln(9) / ln (7))
This country is shaped like a boot and is home to Rome.
What is Italy?
John set up a bank account to save money. He has $1600 and pays 4% annual interest. Write the formula
A(t)= 1600 (1.04)t
What are the first 3 terms of the sequence with the explicit formula, an = 4n2
4, 16, 36
Expand the problem below:
log (xy/√z)
log(x) + log (y) - 1/2 log (z)
Solve for x:
7𝑒4𝑥+2 +3 = 17
x = (ln(2) - 2) / 4
The Amazon Rainforest, the largest rainforest in the world, is mostly in this country.
What is Brazil?
Jon's grandfather was planning to give him $12,000 in 10 years. Jon has convinced his grandfather to pay him $6,000 now, instead. Write the formula, given that Jon invests his money at 7.5% compounded continuously.
A(t) = 6000 (e)0.075*t
Given the sequence 20, 15, 10, ..., -50
What is the explicit formula?
an= 20 - 5(n - 1)
Condense the problem below:
5ln(x+y) − 2ln(y) − 8ln(x)
ln((((x+y)^5)/y^2)/x^8)
Solve for x:
2𝑒3𝑥 +2𝑒4𝑥 = 24
x= (ln(12) / 7)
This South American country’s official language is Portuguese.
What is Brazil?
Lydia's aunt Rose left her $5,000. Lydia spent $1,000 on her wardrobe and deposited the rest
in an account that pays 6.9% compounded daily. How much money will she have in 5 years?
(**Hint: Only set up the equation**)
A(5)= 4000 (1 + (0.069/365))365(5)
Given the sequence 3, 6, 12, 24, 48, 96, …
What is the explicit formula?
an= 3 (2)n-1
Expand the problem below:
ln(x^(4)√(zy^3)
4ln(x) + 1/2(ln(z) + 3ln(y))
Solve for x:
𝑙𝑜𝑔(5𝑥 + 2) ― 𝑙𝑜𝑔(3) = 𝑙𝑜𝑔(𝑥 + 2)
x=2
This country is famous for its pyramids and the Nile River.
What is Egypt?
After a patient takes 400 mg of ibuprofen, it is eliminated so that it decays exponentially. After 1
hour, it is expelled and approximately 58% remains in the body
Find the formula
A(t)= 400(0.58)t
Given in the geometric sequence, a2 = 12, r = -3, Find a3
a3 = -36
What is the change of base formula?
logb(a)=(logx(a)/logx(b))
What does ln(e) equal to?
1
This island nation in Southeast Asia is made up of more than 17,000 islands.
What is Indonesia?
After a patient takes 400 mg of ibuprofen, it is eliminated so that it decays exponentially. After 1
hour, it is expelled and approximately 58% remains in the body.
What is the half life?
(log (0.5) / log (0.58) hours
An arithmetic sequence starts with 4 and increases by 3 each term.
Find the sum of the first 10 terms.
S10 = 175