1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wariber [46]
3 years ago
8

At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

.M. the temperature of the tea is 197°F. At 7:15 A.M. the temperature of the tea is 180°F. Alicia will drink the tea when its temperature is 172°F.
Part A

Which of the following shows an exponential cooling equation that models the temperature of the tea?

A. y = 72(0.989)x + 128

B. y = 128(0.989)x + 72

C. y = 200(0.989)x + 72

D. y = 128(0.989)x + 200

Part B

When can Ella drink the tea?


Ella can drink the tea after
7:22
7:18
Mathematics
1 answer:
NeTakaya3 years ago
6 0

Answer:

Part A

The most correct option is;

b. y = 128(0.989)x + 72

Part B

Ella can drink the tea after 7:22

Step-by-step explanation:

Here we have the temperature variation with time given in an exponential equation as follows;

Let the temperature at time x (in minutes) = y

Therefore, y = a × mˣ + b

Where:

b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞

When y = 200, x = 0

Therefore. 200 = a × m⁰ + c = a + c

We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F

Hence a = 200 - 72 = 128°F

When y = 197, x = 2 minutes

Therefore, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Hence the exponential equation of cooling is presented in the following equation;

y = 128 × (0.98821)ˣ + 72

Therefore, the most correct option is b. y = 128(0.989)x + 72

Part B

When the temperature is 172°F we have;

172 = 128 × (0.989)ˣ + 72

∴ (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Hence Ella can drink the tea after 7:22.

You might be interested in
Round 43,000 to the nearest thousand
Maru [420]
43,000 is the answer, you don't have to round.
8 0
3 years ago
a chalk line is placed around the perimeter of the football field what is the length of this line in feet
masya89 [10]

50 so thatbis the snswer



3 0
3 years ago
Adam wanted to play his video games. His mother told him that he needed to finish his homework, clean out the dishwasher, and cl
Deffense [45]

Answer:

148 minutes = 2h 28 min

Step-by-step explanation:

48min+(25+75mins)=48+100=148

5 0
2 years ago
Twice the sum of a number and 5 is equal to three times the difference of the number and 2
Alexxx [7]

Answer:16

Step-by-step explanation:

Let the number be X

Twice the sum of a number and 5

= 2X+5

Three times the difference of the number and 2

= 3(X - 2)

Since Twice the sum of X and 5 is equal to three times the difference of the X and 2, This means

2(X + 5 )= 3(X - 2)

2X +10 = 3X - 6

3X -2X = 10 + 6 = 16

X = 16

Check

2×(16+5) =3×(16-2)

2×21 = 3×14

42 = 42

3 0
3 years ago
I need help with this
prisoha [69]
D both are right triangles
3 0
3 years ago
Read 2 more answers
Other questions:
  • A rectangle is 5 centimeters longer than it is wide. Find the possible dimensions if the are of the rectangle is 104 square cent
    6·1 answer
  • Round each addend to the nearest whole number and estimate the sum.
    14·1 answer
  • Use the Distributive Property to solve:
    14·2 answers
  • Factor n 3 - n 2 + 3n - 3.
    11·2 answers
  • You are working as a car salesperson at a motor shop. You earn a 2% commission on every car sale, in addition to your wage of $2
    12·2 answers
  • Please help me find the area
    13·1 answer
  • If Arianna turns the stove dial 135 to the right what setting will the dial be on​
    10·1 answer
  • What is a direct proportion.
    12·2 answers
  • Solve. 12. - (-4) = <br>9<br>16<br>17 <br>8​
    9·2 answers
  • your village community group is putting a new fence around the park .you offer to help and measure the distance around the park
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!