Thread: [SOLVED] Exponential Problem...don't know how to do it

I have no idea.

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.

C(t)=

(b) Find the average yearly electrical consumption throughout the 20th century.
Exact: _______________. million megawatt-hours
Decimal (nearest hundreth): __________ million megawatt-hours

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



(d) Without doing the calculation for part (c), how could you have predicted which half of the century the answer would be in?

Well, if someone could at least help me with part a...

Okay, update:

I figured out part A.
C(t)=1.5*e^(.06t)

I think I remember a function for the average in this kind of situation...but of course I can't remember it. Does anyone know it?

average value of f from a to b:
= 1/b-a integral from a to b of f(x)dx

And the decimal answer is 100.61. Does anyone know how to find the exact answer?

I figured out part b.

it's (1/100)*25*(e^(.06*100)-e^(.06*0)).

Now during what year was the electrical consumption closest to the average for the century? The average was 100.61...1900 was 1.5...2000 was 605...

It was 1970. And I just guessed on that one, using my calculator to help me. Hehe.

I'm not really quite sure what part d is asking...

Now here are the choices I'm given:

a) The average consumption is on the upper half of the graph.
b) The t-value for the average consumption is on the right side of the graph.
c) The t-value for the average consumption is on the left side of the graph.
d) The average consumption is on the lower half of the graph.

Originally Posted by UAMA

Now here are the choices I'm given:

a) The average consumption is on the upper half of the graph.
b) The t-value for the average consumption is on the right side of the graph.
c) The t-value for the average consumption is on the left side of the graph.
d) The average consumption is on the lower half of the graph.

It's B. The t-value for the average consumption is on the right side of the graph.

Originally Posted by UAMA

I figured out part b.

it's (1/100)*25*(e^(.06*100)-e^(.06*0)).

whered the 25 come from? i have this same problem