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# Intersection point?

How do you find the point of intersection between the curves y=10(1.12)^x and y=3(1.48)^x

### 2 Answers

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- az_lenderLv 72 months ago
set 10*(1.12)^x = 3*(1.48)^x, and you get

10/3 = (1.48/1.12)^x = (37/28)^x, so then

log(10/3) = x*log(37/28) =>

x = log(10/3)/log(37/28) = 4.31975.

Should be an easy matter to find out the corresponding value of y.

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- nyphdinmdLv 72 months ago
rename the functions

y1 = 10*(1.12)^x y2 = 3*(1.48)^x

Now find x suh that y1 = y2 --> 10*(1.12)^x = 3*(1.48)^x

Take log of both sides

log(10) + x*log(1.12) = log(3) + x*log(1.48) --> solve for x

Note log(10) = 1 so x*(log(1.48) - log(1.12) = 1 - log(3)

x*log(1.48/1.12) = 1 - log(3) ---> x = (1 - log(3))/log(1.48/1.12) = 4.3198

then y1 = y2 = 16.316 --> (4.3198, 16.316) is the intersection point

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