Final answer:
The doubling time, t2 from the given expression, P(t) = (361)^(2/3) is approximately c) (t = 6)
Step-by-step explanation:
The doubling time, t2, can be calculated using the formula: t2 = ln 2/ln(1 + p).
The doubling time represents the time it takes for the quantity to double.
In this case, if we consider p as 1, we can find the doubling time.
Using the approximation that ln(1 + p) is approximately equal to p for small values of p, we can determine that the doubling time, t2, is approximately 70 divided by the annual growth rate, p, in percent.
Applying this formula to the given expression, P(t) = (361)^(2/3), we can find the doubling time.
The exponent, 2/3, represents the growth rate, p.
Substituting this value into the formula, we get:
t2 = ln 2/ln(1 + 2/3) = ln 2/ln(5/3).
t2 = 6.38 or 6.
So therefore the correct answer is c) (t = 6)