Question

Butter is taken out of the fridge and left to warm up. The temperature of the butter, T (in Celsius degrees), after m minutes is given by the equation T=c-k*1.2^{-m}. The initial temperature of the butter is 5º, and after 5 minutes its temperature has increased to 15º, as shown on the graph
a) Find the values of k and c

Answer 1

Yeaa...nope.

@Vocaloid

Answer 2

\(T(m) = c- k \cdot 1.2^{-m}\)

\( T(0) = 5 \implies c = k + 5\)

\(T(5) = 15 \implies c - k ~ 1.2^{-5} = 5 \)

solve from there

Answer 3

\(T(5) = c - k ~1.2^{-15} = 15\)

Answer 4

oh balls :( you get the picture. just plug in the numbers and solve :)

Answer 5

For T(5), I got
\[c=15+\frac{1}{2.48832}k\]

Answer 6

So then I would do
\[k+5=15+\frac{1}{2.48832}k?\]

Answer 7

the key is to write both equations and solve by elimination

5 = c - k(1.2)^(0)
15 = c - k(1.2)^(-5)

you can subtract these two equations to eliminate c

10 = c - k(1.2)^(-5) - [c - k(1.2)^(0)]

after you eliminate c you should be able to solve for k, then back-substitute to get c

Answer 8

ok I got it now

10 = c - k(1.2)^(-5) - [c - k(1.2)^(0)]

10 = -k(1.2)^(-5) + k

k is about 16.719, then you can select one of the initial points, plug in and solve for c

Answer 9

\[ 5=c-16.719*1.2^{-0}\\
c=21.719\]

Answer 10

good

just to be on the safe side I would double-check those k and c values by plugging them back into the points to see if you still get 5 and 15 ;;

Answer 11

\[ 5=21.719-16.719*1.2^{0}\\
5=5\]

Answer 12

Thank you Vocaloid :P

Answer 13

So: here, Completing the Square is a real timesaver.

Not too shabby  😀

Answer 14

Tony is interviewing with the hiring manager for an IT job.

What should he do du

Answer 15

1. Henrietta did an experiment. She started out with 800 bacteria cells. She found that the growth rate of the bacteria cells was 3.

Answer 16

Read the quotation from "To the King's Most Excellent Majesty."

"And may each clime with equal gladness see
A monarch's smile can set his subjects free!"

Answer 17

help me with a math problem please:

Answer 18

Read the quotation from "To the King's Most Excellent Majesty."

u201cGreat God,

Answer 19

i love you

Answer 20

lowell has a credit card that uses the adjusted balance method. for the first 10 days of one of his 30-day billing cycles, his balance was $1360.

Answer 21

I HAVE NO IDEA WHAT TO DO https://screenshots.firefox.com/LaGS1bctHTOBQQgx/docs.google.

Answer 22

help me with a math problem

Answer 23

The function f(x)=5(xu22121) is shown on the coordinate plane.

Select from the drop-down menus to correctly describe the end behavior of u200b f(x) u200b.

Answer 24

Josephine earned a 15% return on her investments last year. If the inflation rate

Answer 25

Emily's credit card has arrived and she has a balance of $2,350. She only has enough money to pay off $1,500.

Answer 26

Craig measured a length as 0.034 millimeters. What is the margin of error?
0.03 mm to 0.

Answer 27

According to the information presented in the lecture, what can be said about personality?
a.

Answer 28

Kyle says sorry.

Answer 29

In the twentieth century, muckraking journalism developed mostly in response to
A) wartime censorship.

Answer 30

my cat just got to a baby lizard but i dont want to put him outside bc i dont want him to die i want to help him.

Answer 31

help with math

Answer 32

Martin Luther King Jr. uses figurative language strategically throughout his letter to promote equality.

Answer 33

Charlie graphs the equation y=u201312x+2 .

Select all statements about Charlie's graph that are true.