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?

410.32

Step-by-step explanation:

Given that the initial quantity, Q= 6200

Decay rate, r = 5.5% per month

So, the value of quantity after 1 month,

The value of quantity after 2 months,

From equation (i)

The value of quantity after 3 months,

From equation (ii)

Similarly, the value of quantity after n months,

As 4 years = 48 months, so puttion n=48 to get the value of quantity after 4 years, we have,

Putting Q=6200 and r=5.5%=0.055, we have

Hence, the value of quantity after 4 years is 410.32.

3201

step-by-step explanation: