Question

Patrick and Brooklyn are making decisions on their bank accounts. Patrick wants to put money in an account that has a higher interest rate but only gains interest for a short period of time. Brooklyn wants to put the money in an account with a lower interest rate, but it gains interest for a longer period of time. Explain which method will result in more money.

Answer 1

i think the lower intrest rate over a longer period of time would make more money.. i just dont know how to explain the method

Answer 2

Well, it really depends on how long they intend to keep their money in the bank account. If they are immortal beings that can watch their money grow forever, then Brooklyn would be correct.

Let's say the bank Brooklyn is interested in is terrible and gives 1 penny every 5 years. Well, if Brooklyn is immortal and can watch her interests grow forever, she'll get infinite money, cause after an infinite number of years she'll have an infinite amount of money.

Answer 3

Of course, no one is immortal and you can't reasonably expect to get an infinite amount of money back from the bank, so it really depends on amounts. If Patrick's bank gives a billion% interest rate and gives them 20 billion dollars every year but only for 1 year, then that's pretty good.

Answer 4

You should explain that it really depends on what the exact rate is and how long they expect to keep their money in the bank for, as extreme examples can be fabricated in support of either side.

Answer 5

That helps a lot thanks! I need help with some more, could you help?

Answer 6

Sure, go ahead.

Answer 7

Lucy has determined a function f(x) that shows the exponential growth of the number of t-shirts Oliver owns each year. Explain how the f−1(x) can be found and what f−1(300) means.

Answer 8

I'm not too familiar with that notation. Is it actually f-1(x) or was that a typo?

Answer 9

oh no its an exponent

Answer 10

both f^-1(x) and f^-1(300)

Answer 11

Oh okay. The caret symbol is usually used to show exponents online

Answer 12

^

Answer 13

Oh okay. Yeah.

Answer 14

i think i can figure it out... but this one ----
Shannon is managing a small zoo and has been analyzing the attendance data. Shannon has found that the number of sleeping animals increases exponentially as the temperature increases. Shannon has also found a linear equation that models the number of people who leave the park early depending on the number of sleeping animals. Describe how Shannon can combine these two functions into a new function and explain what that function would predict.

Answer 15

Okay. If the number of sleeping animals = 2^x (could be different, just using it as an example)

Answer 16

Then we can say the y=2^x where y = the number of sleeping animals.

Answer 17

If r is the number of people leaving the park, and it depends on the number of sleeping animals in a linear fashion

we can say r= y
or r= y + 3
or r= 4y+2

Answer 18

Or something of the sort

Answer 19

We can substitute that back in to the original equation

Answer 20

And find r = 2^x (where x is the temperature)

Answer 21

So we can conclude that the number of people leaving the park increases exponentially as the temperature increases.

Answer 22

wait so what could that function predict if we combine them?

Answer 23

^ What I just typed. Since it is a linear function that combines the sleeping animals/ number of people leaving, the number of people leaving the park increases exponentially as the temperature increases.

Answer 24

Does that make sense? It's like, if somethings are increasing at a related rate, then they both will depend on the same factor.

Answer 25

Ok i undertand now!!

Answer 26

Like, if I drop two bricks that are taped to one another, and we say that the distance that one brick has dropped = the distance the other brick was dropped (since they're taped to each other they depend on each other)

And we know that the distance one brick has dropped increases exponentially as time goes on, then we know that the distance the other brick was dropped also increases exponentially.

Answer 27

Since they are related by a linear equation, they depend on the same thing equally.

Answer 28

yes it does make sense, so ill say, the function that compines the number of animals sleeping and the number of people leaving the zoo increases exponentially as the temperature rises... both equations depend on the same thing, which is the temperature.?

Answer 29

Yes

Answer 30

I'd word it a bit differently, but you seem to have the concept.

Answer 31

this helped a lot thanks :)

Answer 32

Alright no problem. You have a nice day. :)

Answer 33

You too happy holidays :)