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
Damm [24]
3 years ago
15

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

e start of 2014. According to this model, how fast was the population growing at the start of 2014 and at the start of 2015? Give your answers in millions of people per year rounded to 2 decimal places. At the start of 2014, the population was growing at million people per year. At the start of 2015, the population was growing at million people per year.
Mathematics
1 answer:
vitfil [10]3 years ago
6 0

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by P(t)=1.394(1.006)^t

To find the derivative you need to:

\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t

To find the population growing at the start of 2014 we say t = 0

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year

To find the population growing at the start of 2015 we say t = 1

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year

To convert billion to million you multiple by 1000

P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year

You might be interested in
What is the point called where 2 lines intersect or cross? It is the ___________ to the system of equations
Oxana [17]

Answer:

Step-by-step explanation:

The point where the lines intersect is called the point of intersection.These form opposite angles.

7 0
2 years ago
Read 2 more answers
A friend of yours, a senior, took the Graduate Record Exam in September and scored in the 99th percentile. InFebruary, your frie
Alecsey [184]

Answer:

"differential selection"

Step-by-step explanation:

If your friend took the test twice and passed both times with a score above 90% then the minor difference in price is most likely due to "differential selection". The first test had  questions that he had a little more experience in solving, while the second time he was most likely given a couple questions that he wasn't as prepared for as he was the first time. This is most likely the cause for the difference in percentiles.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

3 0
3 years ago
In the diagram, which letter represents the transition from gas to liquid?
Tanya [424]

Answer:

I answered it as C, but the correct answer is B :)

5 0
3 years ago
A box of cereal contains 23.4 ounces. It costs $5.49. What is the cost to the nearest cent of the cereal per ounce
cestrela7 [59]
So in a proportion 23.4 over 5.49 equals 1 over o and multiply 5.49•1=23.4o
5.49=23.4o divide by 23.4 on both sides and that equals 4.26 per oz
3 0
3 years ago
Read 2 more answers
I need help ASAP!!!Please explain how you got your answer
Naddik [55]

Answer:

See the pic below.

Step-by-step explanation:

I erased the incorrect answers and filled in the correct answers with numbers.

7 0
2 years ago
Other questions:
  • What is the sum of the measures of the angles in any hexagon?
    5·1 answer
  • How to find the area of the shaded region
    6·1 answer
  • Brad bought 70.030 m of chain to make necklaces. He used 0.667 m of the chain to make one necklace.
    7·1 answer
  • I need help on the Wednesday column, question 1, letter b.
    14·2 answers
  • Which polygons are congruent?Select each correct answer. Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain o
    15·1 answer
  • a Christian University found that about 3% of its students came from certain state the university had 156 students from that sta
    11·1 answer
  • An X-box game costs $65. You have a $40% off coupon code. After the discount, a 7% sales tax is applied. What is the final cost
    12·2 answers
  • I need help asap! With formula and explanation please!
    13·1 answer
  • ?????????????????<br><br>I need help which one is it<br>help ASAP ​
    5·2 answers
  • The two triangles are similar. Find the unknown variables.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!