Hello I'm a new user on this forum and I've difficulties with this question in my handbook regarding exponential growth.

I'll post the question below and how i would solve it(seems wrong according to my handbook)

In 1990, the chinese population was 3 times as high as the population of europe.

The chinese population rises each year with 2% ,while the population of europe goes down with 0.5%.

When will the chinese population be 4 times as high as the population of europe.

I'd say: 400 * 1.02^{t}= 100 * 0.995^{t}

400/100 = 0.995^{t}/1.02^{t}

log (4) = t*log (0.995) - t*log(1.02)

log (4) = t*(log (0.995) - log(1.02))

log (4)/(log 0.995 - log 1.02) = t = -55.864

This seems to be wrong. According to my handbook the answer is after 11.6 years.

The answer in my handbook is a lot more logical than mine, and I really want to know what I did wrong.

Thanks in advance!