A quantity with an initial value of 6200 decays continuously at a rate of 5.5% per month. What is the value of the quantity after 4 years, to the nearest hundredth?

Answer 1

To solve this problem, we can use the formula for exponential decay:

\[ A = P \cdot e^{rt} \]

where:
- A is the final amount
- P is the initial quantity
- e is the base of the natural logarithm (approximately equal to 2.71828)
- r is the decay rate per time period (in this case, per month)
- t is the time in months

Given:
- P = 6200
- r = 5.5% = 0.055
- t = 4 years = 4 * 12 = 48 months

Substitute these values into the formula:

\[ A = 6200 \cdot e^{0.055 \cdot 48} \]

\[ A = 6200 \cdot e^{2.64} \]

\[ A \approx 11518.68 \]

Therefore, the value of the quantity after 4 years, to the nearest hundredth, is approximately 11518.68.