Help! This really makes NO sense to me. I\'m changing the numbers of the rate fo

Question

Help! This really makes NO sense to me. I'm changing the numbers of the rate for human population because I want to find the real answers on my own SO please explain how you do this. Thanks!

For a population growing exponentially, consider the relationship btwn doubling time and loge? as shown in this example:

loge? t2
.01 69.0
.02 34.5
.03 23.0
.04 17.3
.05 13.8

So, if a colony of bacteria is increasing by a rate of .02/minute, its doubling time would be approximately 34.5 minutes if it is growing exponentially. (all these numbers are correct so somehow you use this to get 34.5. This is the example part. Here is the question: If a human population were to increase at a rate of 5% a year, its doubling time would be _____________ years.

Would you expect this population of bacteria in your lab to grow at the same rate for decades beyond 2209? Why or why not? - this I'm going with no- because eventually a population will reach carrying capacity.....

We received an earlier equation of... t2= loge2=0.69 both underlined and underneath:
loge? loge?
This equation is very confusing. Doubling time is t2 (how long it takes N to be 2N)

Explanation / Answer

Doubling time is the time required to doble the size of a population. It is calculated by using the percentage of growth, r%. Td = log (2) / log (1+ r/ 100) Td = log (2) / log (1+ r%)      = 70 / r     Input the value of r = 5, we get Td = 70/ r = 70 / 5      = 14 (approximately) Therefore the doubling time is 14years. --------------------------------------------------------------------------------------------------------------------- For t2= loge2=0.69 If doubling time is 0.69 years, then the r% is 0.1. The annual growth rate will be 0.1 Td = log (2) / log (1+ r%)      = 70 / r     Input the value of r = 5, we get Td = 70/ r = 70 / 5      = 14 (approximately) Therefore the doubling time is 14years. --------------------------------------------------------------------------------------------------------------------- For t2= loge2=0.69 If doubling time is 0.69 years, then the r% is 0.1. The annual growth rate will be 0.1

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