# exponential growth

• Dec 13th 2006, 07:27 PM
cyberdx16
exponential growth
Tooth size reduction now has a rate of 1% per 1000yrs

A) if t represents time in years and y represents tooth size, use the condition that y=yo.(99) when t=1000 to find the value of k in the equation y=yoe^kt. then use k in B

so k=.00001

B) in about how many years will human teeth be 90% of their present size?
• Dec 14th 2006, 12:00 AM
earboth
Quote:

Originally Posted by cyberdx16
Tooth size reduction now has a rate of 1% per 1000yrs

A) if t represents time in years and y represents tooth size, use the condition that y=yo.(99) when t=1000 to find the value of k in the equation y=yoe^kt. then use k in B

so k=.00001

B) in about how many years will human teeth be 90% of their present size?

Hello,

from $\displaystyle 0.99 \cdot y_0=y_0 \cdot e^{k \cdot 1000}$ I got:

k = - 0.00001005. I'll use this value for further calculations.

to B) $\displaystyle 0.90 \cdot y_0=y_0 \cdot e^{-0.00001005 \cdot t}$

First divide by y_0 and then solve for t:

$\displaystyle t=\frac{\ln(0.9)}{-0.00001005} \approx 10,483.6 \text{ yrs}$

That means: In round about 10500 years the teeth have only 90% of the initial size.

EB