Question

as of 1995, the human population was expected to double within 50 years. if we calculated r for the human population, we would get 1.39. true false

Explanation:

Step1: Use the formula for exponential growth

The formula for exponential growth is \(N = N_0e^{rt}\), where \(N\) is the final population, \(N_0\) is the initial population, \(r\) is the growth rate, and \(t\) is time. If the population doubles, \(N = 2N_0\). So, \(2N_0=N_0e^{rt}\). Dividing both sides by \(N_0\) gives \(2 = e^{rt}\).

Step2: Solve for \(r\)

Take the natural logarithm of both sides: \(\ln(2)=\ln(e^{rt})\). Since \(\ln(e^{x}) = x\), we have \(\ln(2)=rt\). Given \(t = 50\) years, \(r=\frac{\ln(2)}{t}\). Substituting \(t = 50\), \(r=\frac{\ln(2)}{50}\approx\frac{0.693}{50}=0.01386\approx0.0139\) (not \(1.39\)).

Answer:

B. False