Question 21493
Hello There:

To solve this problem algebraically, we need to know a property of logarithms.

ln(a*b) = ln(a) + ln(b)

In other words, if we take the natural log of a product, that is the same as adding the natural logs of the factors.

We need to find the value of x such that f(x) = g(x).

17.5*e^(0.0006*x) = 14.1*e^(0.0187*x)

Take the natural log of both sides.

ln[17.5*e^(0.0006*x)] = ln[14.1*e^(0.0187*x)]

Now use the property described above to write each side as a sum of natural logs.

Remember that ln(e^x) = x, so ln[e^(0.0006*x)] = 0.0006*x.

ln(17.5) + 0.0006*x = ln(14.1) + 0.0187*x

Group like terms; subtract 0.0006*x and ln(14.1) from both sides.

0.0181*x = ln(17.5) - ln(14.1)

Use a calculator to evaluate the expression on the right side.

0.0181*x = 0.2160

Solve for x.

x = 11.9

Adding 12 years to 1998 gives the desired result.

~ Mark