with solution
Q(t) = Q 0 e−0.00012t(where Q 0 is the original amount). We are asked to find t when Q(t) = 0.25Q 0.
Rounding to the nearest 500 yr, we see that the animal died approximately
11,500 yr ago.
Example 17 __
In 1970 the world population was approximately 3.5 billion. Since then it has
been growing at a rate proportional to the population, and the factor of
proportionality has been 1.9% per year. At that rate, in how many years would
there be one person per square foot of land? (The land area of Earth is
approximately 200,000,000 mi^2 , or about 5.5 × 10^15 ft^2 .)
SOLUTION:
If P(t) is the population at time t, the problem tells us that P satisfies the
equation . Its solution is the exponential growth equation
P(t) = P 0 e0.019t,where P 0 is the initial population. Letting t = 0 for 1970, we have
3.5 × 10^9 = P(0) = P 0 e^0 = P 0.