Represent the following expression using an exponent

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

Chang drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would he need to drive 357 miles?

qwelly [4]

Answer:

<h2>15.3 gallons</h2><h2 />

Step-by-step explanation:

ratio and proportion

<u>420 miles </u> = <u> 357 miles</u>

18 gallons x gallons

420 (x) = 357 (18)

x = 6426 / 420

x = 15.3 gallons

4 0

3 years ago

Read 2 more answers

Please Help..............

Anvisha [2.4K]

Well to do scientific notation u have to use 10 then an exponent
example:
2.9867 x 10^10= 29,867,000,000
so u need exponents to do scientific notation.

7 0

3 years ago

A bag contains 5 red, 6 green, 7 yellow, and 8 blue jelly beans. A jelly bean is selected at random. What is the probability tha

Slav-nsk [51]

Answer:

4/13 is the probability does a blue Jelly Bean is selected

Step-by-step explanation:

sample space = sum of all the jelly beans in the bag

sample space =5+6+7+8

sample space =26

probability = Jelly Bean selected / sample space

probability =8/26

probability =4/13

4 0

3 years ago

Please help me and read this carefully

In-s [12.5K]

Answer:

if the subway is an auto mobile, then b , if not then c

Step-by-step explanation:

hope this helps, if not lets talk in the comments

BRAILNLEST PLZZZZZ

7 0

3 years ago