Exponential Equations
2x+3 = 22x + 5
What is x = -2?
How do we do a reflection in the y-axis? Use terminology from the formula y = a(k(x-d)) + c.
What is make the value of k negative?
What is the difference between a series and a sequence?
What is series deals with sums, sequence deals with patterns?
You want to buy AirPods but you are broke. You go to your local bank and borrow $510. You need to pay them within 2 months, and the interest rate is 19%. How much do you need to pay the bank at the end of the term?
What is $526.15?
2x = 19 (Round to two decimal places).
What is 4.25?
What is the mapping rule formula for exponential functions?
What is y = a⋅bk(x-d)+c?
Here is the pattern: 3, 7, 11, 15, 19.... Find the sum of the first 8 terms.
What is 136?
Steve invests in a local bank, to get golden apples. He invests $10,000 at a compounded rate of 6.25% bi-annually. How much will his investment be worth in a year? Round to two decimal places.
4x+3 = 162x+3(64)6(x + 1)
What is x = -1?
What are the transformations on this function, if the original function was f(x) = (1/2)x:
h(x) = (1/2)(-x-3)-4
What is:
- reflection in the y-axis
- horizontal shift 3 units to the left
- vertical shift 4 units down
March 14 is Pi Day! In the dedication of Pi Day, Maple created a pie pyramid that contains 20 rows of pies. The first row of pies contains 3 pies, and each row after has double the pies in the previous row. How many pies are there in total?
What is 3,145,725 pies?
Paran plays and invests into Genshin Impact. Genshin Impact gave him an incredible offer in which Paran will need to invest $250 per 3 months, and Genshin Impact will take the money at a 2.5%/a compounded quarterly. After 2 years, Genshin Impact gets sued, and Paran receives his money back. How much is his money worth? (Round to 2 decimal places).
What is $2,044.30?
A 300g sample of radioactive polonium has a half-life of 60 days. This means that every 60 days, the sample size is half the original. Find the mass of the substance that remains after 75 days. (Round to two decimal places)
What is 126.13g?
If f(x) = 3x is transformed into g(x) = -2(3)(4x + 8) + 2, and if (3, 27) lies on f(x), what is transformed point on g(x)?
What is (-5/4, -52)?
The third term in a geometric sequence is 21 and the ninth term in the same geometric sequence is 1344. What is the sum of the first 3 numbers in the geometric sequence? Represent in fraction form.
What is 147/4?
What is $4,558.78?
A yacht costs $240,000 on sale. It loses 5% of its value each month after it is purchased. Determine when the yacht's value goes under $200,000 in months. (Round to the nearest whole month).
What is 4 months?
What transformations are needed to be applied to
h(x) = 3(2)(-x+3)+1 in order for the function to change to g(x) = 9(2)(3x+3)+1.
What is
- vertical stretch by a factor of 3
- reflection in the y-axis
- horizontal stretch by a factor of 1/3
- vertical shift 2 units down
The arithmetic sequence is as follows, x + 2, 5x, 6x - 2... Find the value of x.
What is x = -4/5?
Elaine wants to buy nitro on discord for 100 people in her gaming server. She decides to invest $500 dollars per 6 months compounded 3.4%/a semiannually. Her annuity is $10,000 by the end of the term. How many compounding periods were there? Round up to the nearest whole number.
What is 18 periods?
Pascal's triangle is dumb according to Einstein. He wants to use the formula for something useful. And that is of course expanding. One of his scientific formulas is (x + y + z)3, try expanding this and make it simpler?
What is x3 + 3x2y + 3x2z + 3xz2 + 3yz2 + 3xy2 + z3 + 3y2z + 6xyz +y3?