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IRISSAK [1]
3 years ago
11

Is the student correct?​

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
6 0
Yes the student is correct
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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 &lt; 5(–3 – 8k)<br> -4 -3<br> -2<br> -1<br> 0<br> 2<br> 3<br> 4<br> 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
2 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
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