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DENIUS [597]
1 year ago
5

The plot below shows the graphs of three functions, f, g, and h, all of which determine the population of three different cities

(in thousands of people) in terms of the number of years x since 2000.The population of City A in 2000 was 40 thousand people and the population increased by 13% each year. The function f determines the population of this city (in thousands of people) in terms of x.Write a function formula for f.f(x)=The population of City B in 2000 was 40 thousand people and the population increased by 16% each year. The function g determines the population of this city (in thousands of people) in terms of x.Write a function formula for g.g(x)=The population of City C in 2000 was 40 thousand people and the population increased by 10 thousand people each year. The function h determines the population of this city (in thousands of people) in terms of x.Write a function formula for h.h(x)=
Mathematics
1 answer:
monitta1 year ago
7 0

So, here we have an exponential function.

Remember that an exponential function has the form:

y=a(b)^x=a(1\pm\frac{r}{100})^x

Where a represents an initial amount, and r is the rate of this amount to change. (Increase, or decrease).

So, given that the population of City A in 2000 was 40 thousand people and the population increased by 13% each year, we can say that

\begin{gathered} a=40 \\ b=1+\frac{13}{100}=1.13 \end{gathered}

So,

f(x)=40(1.13)^x

For city B:

\begin{gathered} a=40 \\ b=1+\frac{16}{100}=1.16 \\ g(x)=40(1.16)^x \end{gathered}

But something different happens with city C. This is not an exponential function, this is a linear function.

So,

h(x)=40+10x

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Answer:

dL/dt  = - 2,019 m/h

Step-by-step explanation:

L²  =  x²  +  y²   (1)    Where  x, and  y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then  dx/dt =  2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

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L*dL/dt  = x*dx/dt + y*dy/dt         (2)

When  the base is 9  and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)²       ⇒    L = √565       ⇒  L  = 23,77

Therefore we got all the information to get dL/dt .

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