exponential function problem

one weird problem:

Throughout much of the 20th century, the yearly consumption of electricity in the US increased exponentially at a continuous rate of 4% per year. Assume this trend continued and that the electrical energy consumed in 1900 was 2 million megawatt-hours.

(a) Write a formula for yearly energy consumption, C, in millions of megawatt-hours as a function of time, t, in years since 1900.

(b) Find the average yearly electrical consumption throughout the 20th century.

(c) During what year was electrical consumption the closest to the average for the century?


for the part (a) I tried "C=2*(1.04)^(t-1900)" but it says wrong. So I couldn't go further...

thanks,
Tuugii

Hello, Tuugii!

Quote:

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Throughout much of the 20th century, the yearly consumption of electricity
in the US increased exponentially at a continuous rate of 4% per year.
Assume this trend continued and that the electrical energy consumed
in 1900 was 2 million megawatt-hours.

(a) Write a formula for yearly energy consumption, , in millions of megawatt-hours
as a function of time, , in years since 1900.

---

Get it? . . . is the number of years since 1900.

For the year 1920, we do not enter . . . We enter

thanks a lot! very much appreciated!

I had a similar problem, although it went like this:
Throughout much of the 20th century, the yearly consumption of electricity in the US increased exponentially at a continuous rate of 6% per year. Assume this trend continued and that the electrical energy consumed in 1900 was 1.5 million megawatt-hours.

(a) Write a formula for yearly energy consumption, C, in millions of megawatt-hours as a function of time, t, in years since 1900.

Aaand...I don't know how to do that.

Soroban made my confusion clear about the year numbers, but his answer was wrong. Since it says continuous exponential rate, you need to use the number e.

so the answer for the part a is gonna be:

C=1.5*e^[0.06t]

I hope this helps. :)

ohmygosh THANK YOU. I've been trying for an hour at least to figure it out! Thank you SO much!:):):):):):)

Quote:

---

Soroban made my confusion clear about the year numbers, but his answer was wrong. Since it says continuous exponential rate, you need to use the number e.

so the answer for the part a is gonna be:

C=1.5*e^[0.06t]

I hope this helps.

---

Soroban is very clever. You should be very careful before contradicting him.

Try substituting t=1. At this point the amount of electricity should have grown by 6% (or 4%, depending on which problem you are doing). Soroban's solution will satisfy this and yours will not.
It is not necessary to involve e to make an exponential function continuous: any positive base will produce a continuous function.