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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

24) 28 + 3k < 5(–3 – 8k) -4 -3 -2 -1 0 2 3 4 5 6

ahrayia [7]

Answer:

k < - 1

Step-by-step explanation:

28 + 3k < 5(-3-8k)

28 + 3k < - 15 - 40k

28 + 15 < - 40k - 3k

43 < - 43k

43/- 43 > k (switch signs because 43 is negative)

k < -1

6 0

3 years ago

Tony has 7/8 of a candy bar he wants to split the bar into servings that are 3/10 of the bar how many servings can he make

Irina-Kira [14]

Answer:

35/12 servings

Step-by-step explanation:

(7/8)/(3/10)=(7/8)(10/3)=70/24=35/12

3 0

2 years ago

Claire is attending a university where tuition for one year costs $18,500. She has a scholarship worth $3,500 per year. She earn

ludmilkaskok [199]

B. 57,800

14,300+14,400+14,500+14,600=$57800

4 0

3 years ago

Read 2 more answers

Can you help me please?

Alisiya [41]

Answer:

The correct answer is : C

Step-by-step explanation:

7 0

3 years ago

Is the student correct?​

Is the student correct?