Question

Eric made a $4500 purchase on his credit card that has an annual interest rate of 13% which compounds continuously. If he did not make a payment for an entire year, how much does he owe? Round your answer to two decimal places

Answer 1

????????

Answer 2

@CO_oLBoY

Answer 3

Use the formula for continuous compounding of interest.\[A = Pe ^{rt}\]

Answer 4

To use this formula substitute the original amount ($4500) for P, e is a constant and is the base for natural logs. The exponents are r which is the interest rate (13% or .13) and t is the amount of years in your case just 1. Plug those values and solve.

Answer 5

divide?

Answer 6

@radar

Answer 7

585?

Answer 8

There is no dividing mostly multiplying rt is .13 times 1 or .13 it would look like this\[A = 4500e ^{.13}\]

Answer 9

so 4500 times 13?

Answer 10

346.15?

Answer 11

No it is 4500 times e to the .13 power. You will need to use your calculator.
e = 2.71828.

\[A=4500\times 2.71828^{.13}\]

Answer 12

2.71828 to the 13 is 35.33764

Answer 13

That is .13 there is a decimal point just to the left of the 1 in .13 (13%)

Answer 14

i mean .13

Answer 15

thats the answer I got 35.33764

Answer 16

I get the value for \[2.71828^{.13}=1.138828284\]

Answer 17

ok is 1.138828284 the answer

Answer 18

It is obviously going to be less than 4 and much less than 35.

Answer 19

would it be rounded like this 1.139?

Answer 20

No multiply that by $4500.

Answer 21

multiply 1.138828284 by 4500?

Answer 22

That means his original debt of $4500 has now increased to $5124.727 or about 625 dollars of interest in one year no less!!

Answer 23

yes multiply.

Answer 24

5,124.72726?

Answer 25

Yes, gain confidence through practice.

Answer 26

is that what its rounded too?

Answer 27

or is it 5,124.73?

Answer 28

Round it to cents, that looks good to me.

Answer 29

ok good

Answer 30

In compound interest you will eventually be working with natural logs.

Answer 31

can you help me with another?

Answer 32

I don't know until I see it, I am not infallible.

Answer 33

A colony of bacteria grows at an exponential rate according to the function
P(t) = 2250e^0.11t which describes the number of bacteria P at time t (in hours).

Find the following:
(A) Find the number of bacteria at t = 0 hours.
number of bacteria =

(B) Find the growth rate of the colony. Round your answer to two decimal places.
growth rate =

(C) Find the population after 10 hours.
population =

(D) When will the population double?
Round your answer to one decimal place.
time = hours

(E) At what time will the population reach 7000?
Round your answer to one decimal place.
time = hours

Answer 34

lol ok me neither this stuff is so confusing!

Answer 35

Well that is quite a problem. First do know how to use logs?

Answer 36

no I dont

Answer 37

I am surprised you would be expected to know how to solve these,,,,,,unless you are good at using the functions on your calculator. Are you adept at using your calculator?

Answer 38

yea i have an online algebra calculator

Answer 39

O.K Lets try the first part I want to be sure I have the correct function for that bacteria>\[P(t)=2250e ^{0.11t}\]. Is that correct?

Answer 40

ok hold on

Answer 41

it wants to know if I should factor it or find the symmetry

Answer 42

or all these other options?

Answer 43

That is saying the population of the bacteria as a function of time (t) is that equation.
A. Population at time 0 (t=0). That one is easy because e to the 0 power is one 1 as is anything to the 0 power is, so the population initially is 2250 bacteria, but as time goes by it will grow according to the equation provided in the problem. For part A you will not need to factor or seek symmetry.

Answer 44

ok then It wont give me a topic

Answer 45

so I cant use the calculator

Answer 46

Yes, and did you understand the solution for Part A.??

Answer 47

not really

Answer 48

2250 divide into 0.11

Answer 49

If t=0 what is 0.11times 0 is what?

Answer 50

0.11

Answer 51

No! anything times 0 is 0