Question 60178This question is from textbook Applied College Algebra
: The population P of India can be modeled by the equation P(t) = 368(1.02)^t, where t is the number of years since 1950 and P is given in millions.
a. Use the function to estimate the population of India in the year 2010. Round to the nearest milion.
b. Use the function to determine the year during which the population of India will reach 2 billion.
This question is from textbook Applied College Algebra
Answer by chitra(359)  (Show Source):
You can put this solution on YOUR website! Given P (t) = 368 * (1.02)^t
r = 10^m
1.02 = 10^m
Taking log on both sides, we get:
Log(1.02) = m log(10)
0.008600 = m (1)
A = 10^b
368 = 10^b
Taking log on both sides, we get:
Log(368) = b (log 10)
2.56584 = b
y = mx + b
y = 0.0086 x + 2.56584 --------- EQN(1)
Put x = 60 ( 1950 + 60 = 2010 ) in the above equation, we get
y = 0.0086 (60) + 2.56584 = 0.516 + 2.56584 = 3.08184
y ≈ 3. 1 million
b. Use the function to determine the year during which the population of India will reach 2 billion.
Solution: Consider the equation (1), we get:
y = 0.0086 x + 2.56584
When y =2 billion,
2 = 0.0086 x + 2.56584
-0.56584 / 0.0086 = x
-65.795 = x
The year when the population will be 2 million is
1950 - 65.79 = 1885
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