Question

Use the fact that the world population was 2560 million people in 1950 and 3040 million in 1960 to model the population of yhe world in the second half of the 20th century. (Assume that the growth rate is proportional to the population size.) What is the relative growth rate k? Use the model to estimate the world population in 1993 and to predict the population in the year 2020.​

Answer 1

Step-by-step explanation:

We measure the time tt in years and let t=0t=0 in the year 19501950. We measure the population P(t)P(t) in millions of people.

Then P(0)=2560P(0)=2560 and P(0)=3040P(0)=3040

P(t)=P(0)ekt=2560ektP(t)=P(0)ekt=2560ekt

P(10)=2560ekt=3040P(10)=2560ekt=3040

This is where I have a problem.

I apply the natural logarithm to both sides of the equation.

ln2560e10k=ln3040ln⁡2560e10k=ln⁡3040

I move the exponent up front. I am not sure if I am allowed to move the constant and variable.

10k ln2560e=ln3040