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4 years ago

Please help me out here! Only B, not A.

Mathematics

1 answer:

Eduardwww [97]4 years ago

4 0

I entered into a graphing website and this is what I got. :)

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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

vitfil [10]

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

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

6 0

3 years ago

Pleaseee helpppp last question

kap26 [50]

Answer: y=-4x-3

Step-by-step explanation:

just draw all the lines on a graph

8 0

3 years ago

How many solutions does this equation have?<br><br> –4j = –8j + 4j

emmainna [20.7K]

Answer:

Your Mom just remember your a di*k and thats why your parents burned your birth certifcate

Step-by-step explanation:

if your gonna do that to me, remember i have copy and paste<3.

5 0

3 years ago

Please help me with my classwork

marshall27 [118]

Answer:

Use calculator

Step-by-step explanation:

Use your calculator, put the number in front of the square root, then use 2nd then hit the button below math to get the square root on your calculator.

4 0

3 years ago

Brittany has a gift box in the shape of a cube. Each side of the box measures 15 cm. what is the volume of the gift box?

miss Akunina [59]

The formula for the volume of a cube is:

v=s³

Where v=volume and s=the length of a side

Since we know that the length of a side of the gift box is 15cm, we can solve for the volume.

v=15³=3375cm³

Answer: V=3375cm³

7 0

3 years ago

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