Helps in Calculus question? ?

Question

The U.S is China's largest export market. Imports from China have grown from about 8 billion dollars in 1988 to 39 billion dollars in 1995. This growth has been approximately linear

a)Use the given data pairs to write a linear equation that describes this growth in imports over the years. Let x=88 represent 1988 and x=95 represent 1995.

b)When will imports reach 50 billion dollars?

Please show me how to do it, Thankss!!!!!

Answer 1

Your imports have grown 31 billion in 7 years. If the growth was linear then you are growing by 31/7 billion per year

Let Y be the year that you surpass 50 billion. In other words you need to gain 11 billion dollars more. So 31$/7*Y > 11$ so Y > 77/31 so it is only 3 years more or the year 1998.

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As an equation just do the ratio (x-95)/(D-39)=(95-88)/(39$-8$)

x=95+(D-39)*7/31

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It would be highly unlikely that such growth would be linear, It is more likely that it would be logarithmic. Did you mean logarithmic?

Answer 2

x1= 88 y1= 8 x2= 95 y2= 39

slope = (y2-y1)/(x2-x1)

= (39-(8))/(95-(88))

= (39-8)/(95-88)

slope= 31/7

b = (y1-m*x1)

b =8-[(31)/(7)](88) = -381.7143

Equation: y= mx +b , m = slope

Equation of the line is : y = (31/7) x -381.7143

b)

50 = (31/7) x -381.7143

(31/7)x = 50+381.7143

(31/7)x =431.7143

x= (431.7143)(7) / 31 =97.48

In 1997, it would have reached 50 billion dollars.

Answer 3

a) m=(39-8)/(95-88)=31/7

y-y1=m(x-x1)

y-8=31/7(x-88)

b)50-8=31/7(x-88)

364/31=(x-88)

364/31+88=x

x=~99.741

imports reach 50 billion dollars in 2000.