The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time. The town consumed 4.44.44, point, 4 trillion British thermal units (BTUs) initially, and it consumed 5.55.55, point, 5 trillion BTUs annually after 555 years. What is the town's annual energy consumption, in trillionso f BTUs, after 9 years?

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

Step-by-step explanation:

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.

This means that the consumption after t years is given by the following differential equation:

In which k is the growth rate.

The solution is, applying separation of variables:

In which C(0) is the initial consumption.

The town consumed 4.4 trillion British thermal units (BTUs) initially.

This means that

So

5.5 trillion BTUs annually after 5 years.

This means that . We use this to find k. So

So

After 9 years?

This is C(9). So

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.