Linear Law Problem.

Question

Q: A law of the form y=ab^x relates x and y.
From a set of readings, lg y is plotted against x to give a
straight line with gradient and vertical intercept both 1.5 each.
Deduce the value of a and b.

ANS; a = 120 
   ; b = 10

I've tried putting lg on both sides for y=ab$^x$ and got: lg y = lg a + x lg b. I guess y-intercept = lg a and gradient = lg b ? Also, I tried comparing:

lg y - 1.5x - 1.5 == lg y - lg a - (lg b)x

I can't get further.

Actually the solutions are wrong, some error occured. The answers for a and b are ;lg a = 1.5; & ;lg b = 1.5;

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score 1 · Accepted Answer · answered Sep 23 '18 at 22:11

You've done the correct thing in taking logarithms. We have $$\ln y = \ln a + x\ln b.$$ (Note that any logarithm base will do, but just run with this.) We're given that the slope (gradient) is $1.5$. So $\ln b = 1.5$. The y-intercept is also given so $\ln a = 1.5$. The result follows.

I'm not sure why the answer key gives the answers as such. It is possible it could be a typographical error.

Linear Law Problem.

1 Answers1