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Helen [10]
3 years ago
10

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?
Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0

Answer:

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:

\frac{dC}{dt} = kC

In which k is the growth rate.

The solution is, applying separation of variables:

C(t) = C(0)e^{kt}

In which C(0) is the initial consumption.

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

This means that C(0) = 4.4

So

C(t) = C(0)e^{kt}

C(t) = 4.4e^{kt}

5.5 trillion BTUs annually after 5 years.

This means that C(5) = 5.5. We use this to find k. So

C(t) = 4.4e^{kt}

5.5 = 4.4e^{5k}

e^{5k} = \frac{5.5}{4.4}

e^{5k} = 1.25

\ln{e^{5k}} = \ln{1.25}

5k = \ln{1.25}

k = \frac{\ln{1.25}}{5}

k = 0.0446

So

C(t) = 4.4e^{0.0446t}

After 9 years?

This is C(9). So

C(9) = 4.4e^{0.0446*9} = 6.57

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

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