Answer:
Step-by-step explanation:
Formula for the exponential graph is given by the function,
[tex]P(t) = P_0(1 + r)^t[/tex]
Where [tex]P(t)[/tex] = population after 't' years
[tex]P_0[/tex] = Initial population
r = rate of increase
t = Number of years
In 1988, population of a country C was 30 million.
A). Function for the population will be,
[tex]P(t)=38(1+0.01)^t[/tex]
[tex]=38(1.01)^t[/tex]
B). Population in year 2020,
[tex]P(22)=38(1.01)^{22}[/tex]
= 47.30 million
C). Doubling time means the duration in which [tex]P_0[/tex] becomes [tex]2(P_0)[/tex].
[tex]P(t)=2P_0[/tex]
[tex]2P_0=P_0(1.01)^t[/tex]
[tex](1.01)^t=2[/tex]
By taking log on both the sides of the equation,
t[log(1.01)] = log2
t = [tex]\frac{\text{log}(2)}{\text{log}(1.01)}[/tex]
= [tex]\frac{0.30103}{0.004321}[/tex]
t = 69.66 years
