MHT CET · Maths · Differential Equations
The rate of increase of the population of a city is proportional to the population present at that instant. In the period of 40 years the population increased from 30,000 to 40,000 . At any time \(t\) the population is \((a)(b)^{\frac{t}{40}}\). Then the value of \(a\) and \(b\) are respectively
- A \(30,000, \frac{2}{3}\)
- B \(30,000, \frac{4}{3}\)
- C \(40,000, \frac{2}{3}\)
- D \(40,000, \frac{3}{4}\)
Answer & Solution
Correct Answer
(B) \(30,000, \frac{4}{3}\)
Step-by-step Solution
Detailed explanation
\(P(t) = a \cdot b^{\frac{t}{40}}\) \(P(0) = 30,000 \Rightarrow a \cdot b^0 = 30,000 \Rightarrow a = 30,000\)
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