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3 years ago

Inverse function of f(x) = 1/9x + 10/9

Mathematics

1 answer:

Gelneren [198K]3 years ago

8 0

The answer to this function is M = 1/9 (The slope is "M").

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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

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

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3 years ago

Diego is building a kitchen table and a coffee table. The legs of a kitchen table must be twice the height of a coffee table and

GuDViN [60]

B. They are twice as long and there are 4 of them

7 0

4 years ago

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a cell phone company charges $42 per month of service the cost of a new cell phone plus 8 months of service is $415.99 how much

salantis [7]

1247.97 so you have to skip count

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3 years ago

Find x and y part 4 for these problems

Dvinal [7]

Answer:

Step-by-step explanation:

3) Sin30 = 11/x

x = 11/Sin30 = 11/0.5

x = 22

Tan 30 = 11/y

y = 11/tan30 = 11/0.5774

y = 19.1

4) Sin30 = 6/x

x = 6/Sin30 = 6/0.5

x = 12

Tan 30 = 6/y

y = 6/tan30 = 6/0.5774

y = 10.39

5) Sin45 = 9√2/y

y = 9√2/Sin45 = 9√2/(√2/2) =

9√2 × 2/√2 = 18

x = 18

Tan 45 = 9√2/x

x = 9√2/Tan 45 = 9√2/1

x = 9√2

Sin60 = 9/x

x = 9/Sin60 = 9/0.866

x = 10.39

Tan 60 = 9/y/2 = 18/y

1.7321 = 18/y

y = 18/1.7321

y = 10.39

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3 years ago

Kalani bought 2.5 pounds oranges for $1.58 per pound.how much did kalani spend on oranges ?

Tcecarenko [31]

To find the answer for this simply multiply 2.5 by 1.58

2.5 x 1.58= 3.95

So Kalani spent a total of $3.95 on oranges!

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3 years ago

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