Answer:
a.[tex]p = 2.519*(1.0177^{t})[/tex]
b.[tex]t =\frac{log(\frac{p}{2.519}) }{log(1.0177)}\\[/tex]
c. in the year of 2029
Step-by-step explanation:
The world population in 1950 was 2,519 million or 2.519 billion.
a-) Population after 1950 can be defined as a compounded growth at the rate of 1.77% per year. This can be modeled as follows:
[tex]p = 2.519*(1.0177^{t})[/tex]
b-) To find an expression for the number of years to reach a population p, we must apply logarithmic properties to the expression found in part a. as follows:
[tex]p = 2.519*(1.0177^{t})\\log(p) = log(2.519*1.0177^{t})\\log(p) = log(2.519) + log(1.0177^{t})\\log(p) = log(2.519) + t*log(1.0177)\\\\t = \frac{log(p) - log (2.519)}{log(1.0177)} \\t =\frac{log(\frac{p}{2.519}) }{log(1.0177)}[/tex]
c-) For p = 10:
[tex]t =\frac{log(\frac{10}{2.519}) }{log(1.0177)}\\t = 78.58[/tex]
The model predicts that the world population will surpass 10 billion in roughly 79 years from 1950, that is in the year of 2029.
