# Math

posted by on .

he world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at the rate of approximately 2%/year and find the function Q(t) that expresses the world population (in billions) as a function of time t (in years), with t = 0 corresponding to the beginning of 1990. (Round your answers to two decimal places.)
(a) If the world population continues to grow at approximately 2%/year, find the length of time t0 required for the population to double in size.
t0 = yr

(b) Using the time t0 found in part (a), what would be the world population if the growth rate were reduced to 1.6%/yr?
billion people

• Math - ,

Q(t) = 5.3 + 0.02*5.3t,
Q(t) = 5.3 + 0.106t.

a. Q(t) = 5.3 + 0.106t = 10.6 Billion,
5.3 + 0.106t = 10.6,
0.106t = 10.6 - 5.3 = 5.3,
t = 50 years.

b. Q(t) = 5.3 + 0.016t*5.3,
Q(t) = 5.3 + 0.0848t.

Q(t) = 5.3 + 0.0848*50 = 9.54 Billion.

• Math - ,

part a is incorrect, the proper answer is:

Q(t)=Qoe^kt
Q(t)= 5.3e^0.02t
2=e^0.02t
ln2=0.02t
t=34.6yr