Growth and Decay

[q_fruit]

This is from my textbook...sans the useless info:

In northern Europeans, tooth size reduction now has a rate of 1% per 1000 years.
a) If t represnts time in years and y represents tooth size, use the condition that y=0.99y₀ when t=1000 to find the value of k in the equation y=y₀e^kt. Then use this value of k to answer the following questions.. etc etc..

So here I am, having no idea what to put in for y or y₀. Please help, thx!

 

[Gene]

y₀=100%
y=99% when t = 1000 so
99=100e^(k*1000)
ln(.99) = k*1000
k=ln(.99)/1000

 

[q_fruit]

Thanks.

What did it means by "use the condition that y=0.99y0"?

 

[Gene]

I missed that sentence. It may give a tooth size as .5 cm in the part you didn't share in which case y = .99*.5cm but the .5 cancels and we get the .99 in any case. y and y₀ would change to cm's but doesn't affect k.