Problema Solution
In 1990, the population of Africa was 643 million and by 2000 it had grown to 813 million.
a.) Use the exponential growth model A=A0 e^kt, in which t is the number of years after 1990, to find the exponential growth function that models the data.
b.) By which year will Africa population reach 2 billion?
Answer provided by our tutors
a.) Use the exponential growth model A=A0 e^kt, in which t is the number of years after 1990, to find the exponential growth function that models the data.
A=A0*(e^(kt))
t is the number of years after 1990
for t=0 we have A = 643 that is
A0*(e^(k*0) = 643 million or A0 = 643 million
for t = 2000 - 1990 = 10 we have A = 813 million that is
A0*e^(10k) = 813
643 e^(10k) = 813
e^(10k) = 813/643
10k = ln (813/643)
k = (1/10) ln (813/643)
k = 0.02346
click here to see the step by step solution of the equation
the function is
A=643*(e^(0.02346t))
b.) By which year will Africa population reach 2 billion?
2 billion = 2000 million
643*(e^(0.02346t))= 2000
by solving we find
t = (1/0.02346)ln(2000/643)
t = 48.4 years after 1990
click here to see the step by step solution of the equation
1990 + 48.4 = 2038.4 or we can round the answer to 2038
by the year of 2038 the population will reach 2 billion.