The Population of a Town is 53217 and Declines Continuously
Mathematics
OpenStudy (anonymous):
PLEASE HELP ME WITH THIS:) MY LAST TEST OF MY SENIOR YEAR!
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OpenStudy (anonymous):
Natalie uses a credit card with a 23.6% APR, compounded monthly, to pay for a hotel stay totaling $748.12. She can pay $300 per month on the card. What will the total cost of this purchase be?
OpenStudy (btaylor):
You will be using the formula: \[A=P(1+r)^{nt}\] P is the intial amount, r is the rate, (.236), t is the time it takes to pay it off, and n is the number of times the interest is compounded per year (here, 12).
OpenStudy (calculusxy):
OpenStudy (calculusxy):
There should be your answer. :)
OpenStudy (btaylor):
We want to know the total cost, but first have to figure out the time it will take to pay it. If she can pay $300 a month, she will pay 300t as the amount, where t is the number of months. So we have: \[300t=748.12(1.236)^{12t}\]
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OpenStudy (anonymous):
HMMMM to help you out here are the answer choices a. $748.12 b. $775.31 c. $923.43 d. $924.68
OpenStudy (btaylor):
Let's assume that she pays it off in 3 months. In that time, the total amount will be $788. (in the equation I put earlier, it should be t/12, not 12t) In those three months, she can make $900 in payments. I would choose B to account that she can have it paid off early.
OpenStudy (anonymous):
thank you @BTaylor what about this one?
OpenStudy (anonymous):
The population of a town is 53,217 and declines continuously at a rate of 1.7% each year. What is the approximate population of the town in 9 years? (5 points) Select one: a. 45,607 b. 45,667 c. 45,075 d. 62,015
OpenStudy (btaylor):
Here, your initial amount is 53217, and the rate is 1-.017 = .983 (because it is going down.) You will use the same equation, so: \[A=53,217(.983)^9=45607\] A is the answer.
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OpenStudy (anonymous):
and this one ?@BTaylor mower for $2,285. It depreciates 1.1% each year. What is the value of the lawn mower after six years? (5 points) Select one: a. $2,138.28 b. $2,259.86 c. $2,272.46 d. $2,440.02
OpenStudy (btaylor):
Here, the rate is 1-.011 = .989. Since I'm not supposed to be giving you test answers :), can you try to plug it in on your own?
OpenStudy (btaylor):
Use this equation: \[Amount=Initial(rate)^{time}\]
OpenStudy (anonymous):
i just tried and and idk how :(
OpenStudy (btaylor):
Fill in the blanks: Your initial amount is _________ dollars. The rate of depreciation is _______ (I gave it to you earlier) The time interval is _______ years.
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OpenStudy (anonymous):
Lily purchased a lawn mower for $2,285. It depreciates 1.1% each year. What is the value of the lawn mower after six years? sorry i cut off some of the question
OpenStudy (btaylor):
The initial amount is $2285. The rate is .989. The time interval is 6 years. Using the formula, you get A as your answer.
OpenStudy (anonymous):
AAAHHH!! THANK YOU SO MUCH IM SO CLOSE TO BEING DONE FOREVER!!! YAYAYAYAY! The population of a city is 75,893 and grows continuously at a rate of 3.6% each year. What is the approximate population of the city in 17 years? (5 points) Select one: a. 91,405 b. 122,340 c. 139,827 d. 139,955 @BTaylor
OpenStudy (btaylor):
Your initial amount is 75,893. The rate is 1+.036 = 1.036. The time interval is 17. Plug those in to the formula I gave your, and you get 138457. That's not one of the answer choices, but I'd choose C.
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OpenStudy (anonymous):
William opens a credit card with an APR of 18.63% compounded monthly. How much is charged in interest this month if his balance is $835? (3 points) Select one: a. $12.96 b. $18.63 c. $44.82 d. $69.58 THANK YOU SO MUCH @BTaylor
OpenStudy (btaylor):
If he has a 18.63% APR, that means that for a year, the interest will add up to $155.56 (=835^.1863). However, since he is paying a portion of this monthly, divide it by 12 to get 12.96. A is your answer.
OpenStudy (anonymous):
@BTaylor oh my gosh i love you <3
OpenStudy (btaylor):
Look under the "earn interest on checking" column. Only the high balance account has that feature, so only that would give interest. D is the obvious answer.
OpenStudy (anonymous):
oh psh... duhhhhhhhh. how about this one? Misha deposited $3,725 into a savings account 22 years ago. The account has an interest rate of 2.2% and the balance is currently $6,012.37. How often does the interest compound? (5 points) Select one: a. daily b. monthly c. quarterly d. annually @BTaylor
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OpenStudy (btaylor):
ooh...this is a good problem. Using the formula: \[A=P(1+r)^{nt}\] we try to solve for n. \[6012.37=3725(1.022)^{22n}\] n is roughly 1, which means it is compounded ANNUALLY.
OpenStudy (anonymous):
A certain business has implemented a new incentive plan whereby an employee earns tokens for every sale they make. For 1 sale, an employee earns 1 token. For 2 sales, an employee earns 6 tokens. For 3 sales, an employee earns 12 tokens. For 4 sales, an employee earns 19 tokens. How many tokens will be earned for eight sales? (4 points) Select one: a. 46 b. 48 c. 53 d. 57
OpenStudy (anonymous):
@BTaylor
OpenStudy (btaylor):
Between 1 and 2, it increases by 5. Between 2 and 3, it increases by 6. Between 3 and 4, it increases by 7. Logically, it would increase by 8, 9, 10, 11, ... So, the sequence would become: 1,6,12,19,27,36,46,57 57 is the reward (D)
OpenStudy (anonymous):
AHHHHHHHH so close!!! @BTaylor
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OpenStudy (btaylor):
A line graph, since it shows trends over time.
OpenStudy (anonymous):
Abigail has deposited $431 in a savings account that earns interest at a rate of 1.8% compounded quarterly. What will the account balance be in 14 years? (3 points) Select one: a. $438.76 b. $476.67 c. $554.21 d. $775.80
OpenStudy (btaylor):
Using the formula again, we get C.
OpenStudy (anonymous):
Barry spent less than $25 on lunch for his co-workers. If burgers cost $3.75 each and sodas cost $1.75 each, which of the following is not a possible combination of burgers and sodas that Barry could have purchased? (3 points) Select one: a. 5 burgers, 2 sodas b. 6 burgers, 1 soda c. 5 burgers, 4 sodas d. 4 burgers, 5 sodas @BTaylor
OpenStudy (btaylor):
If you add the combinations together, choice C is over $25
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OpenStudy (anonymous):
@BTaylor were almost done!
OpenStudy (btaylor):
It's B (Complicated Calc Work)
OpenStudy (anonymous):
Leticia purchased a lawn mower for $5,935. It depreciates 1.3% each year. What is the value of the lawn mower after eight years? (5 points) Select one: a. $5,857.85 b. $5,345.13 c. $6,581.07 d. $5,883.76 LAST ONE!!!! @BTaylor
OpenStudy (btaylor):
It's B. Congrats!
OpenStudy (anonymous):
i only got 2 wrong!
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OpenStudy (btaylor):
good job. I have to go now.
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