A quantity with an initial value of 1000 decays exponentially at a rate of 0.35% every 3 months. What is the value of the quantity after 1 year, to the nearest hundredth?
To solve this problem, we can use the formula for exponential decay:
\[A = A_0 \cdot e^{rt}\]
Where:
- A is the final value of the quantity after time t
- \(A_0\) is the initial value of the quantity
- r is the decay rate
- t is the time in years
Given:
- \(A_0 = 1000\)
- r = 0.35% = 0.0035
- t = 1 year
Plugging the values into the formula:
\[A = 1000 \cdot e^{0.0035 \cdot 1}\]
\[A = 1000 \cdot e^{0.0035}\]
\[A \approx 1000 \cdot e^{0.0035}\]
\[A \approx 1000 \cdot 1.00350347574\]
\[A \approx 1003.50\]
Therefore, the value of the quantity after 1 year is approximately 1003.50.