Need to get these problems checked--
21. Suppose inflation of money is at a rate of 3% per year in the US. How much will a $1 candy bar cost in 30 years?
1.03^30 * 1= $2.43
22. Find the next 3 terms of the geometric sequence 4, 10, 25.
125, 625, 3125? ..Not sure about this.
23. Find the next 2 terms of the geometric sequence 50, 40, 32
128, 512? ..Not sure about this either
24. What is the eighth term of the geometric sequence whose first three terms are 3, 6, and 12?
3 * 2^7 = 384?
28. True or False: Linear and exponential functions are exactly alike.
False.
30. What is the y-intercept of the graph of y = 4^x-2?
-2?
Thanks
-MC
22. the common ratio is 10/4 or 2.5
then 25(2.5) = 62.5
62.5(2.5) = 156.25
156.25(2.5) = .... etc
23. done the same way, find the common ratio 40/50 or 4/5 or .8
the rest are correct
Let's go through each problem and check the answers.
21. Suppose inflation of money is at a rate of 3% per year in the US. How much will a $1 candy bar cost in 30 years?
To find the future value after 30 years, we can use the formula FV = PV * (1 + r)^n, where PV is the present value (in this case $1), r is the annual interest rate (3% or 0.03), and n is the number of years.
Plugging in the values, we get FV = 1 * (1 + 0.03)^30 = $2.43.
So the answer is correct.
22. Find the next 3 terms of the geometric sequence 4, 10, 25.
To find the next term in a geometric sequence, we multiply the previous term by a common ratio. In this case, the common ratio is found by dividing the second term by the first term: 10/4 = 2.5.
So the next three terms would be: 25 * 2.5 = 62.5, 62.5 * 2.5 = 156.25, 156.25 * 2.5 = 390.625.
The answer provided is incorrect. The correct next 3 terms are 62.5, 156.25, and 390.625.
23. Find the next 2 terms of the geometric sequence 50, 40, 32.
Similar to the previous problem, we need to find the common ratio. In this case, the ratio is found by dividing the second term by the first term: 40/50 = 0.8.
So the next two terms would be: 32 * 0.8 = 25.6, 25.6 * 0.8 = 20.48.
The answer provided is correct.
24. What is the eighth term of the geometric sequence whose first three terms are 3, 6, and 12?
Again, we need to find the common ratio by dividing the second term by the first term: 6/3 = 2.
Given that the first term is 3, we can find the eighth term by multiplying the first term by the common ratio raised to the power of (8-1): 3 * 2^7 = 384.
The answer provided is correct.
28. True or False: Linear and exponential functions are exactly alike.
The statement is False. Linear and exponential functions are different. Linear functions have a constant rate of change, while exponential functions have a constant ratio of change.
30. What is the y-intercept of the graph of y = 4^x-2?
To find the y-intercept, we set x to 0 and solve the equation for y. Plugging in x = 0: y = 4^0-2 = 4^-2 = 1/16.
So the y-intercept is 1/16, not -2.
To summarize:
- Problem 21: Correct.
- Problem 22: Incorrect. The correct next 3 terms are 62.5, 156.25, and 390.625.
- Problem 23: Correct.
- Problem 24: Correct.
- Problem 28: False.
- Problem 30: Incorrect. The y-intercept is 1/16, not -2.