Find model for number of unit cases sold as fcn of t, where

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bjackson11

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I am currently taking Brief Calculus class and it's been a while since algebra for me. I am working on a homework problem and I need to create an equation. I fear the only way to make sure that we both understand what I need help on is to write out the entire text of the problem so you will be looking at the same information as me. So here goes;

Company Revenue
In its 2001 annual Report, the Coca Cola Company reported that "Our worldwide unit case volume increased 4 percent in 2001, on top of a 4 percent increase in 2000. The increase in unit case volume reflects consistent performance across certain key operations despite difficult global economic conditions. Our business system sold 17.8 billion unit cases in 2001. A unit case is equivalent to 24 eight-ounce servings of finished beverage.

a) Find a model for the number of unit cases sold (s) as a function of (t), where t is the number of years since 1999.

OK....I understand that this is an exponential growth rate equation. I have an equation of s(t)=17.8(1.04)^t-2 In 1999 t=0, in 2001 t=2. The answer in the back of my book has an equation of s(t)=16.5(1.04)^t

What happened to the exponent of t-2?
 
Re: Derivative Applications

bjackson11 said:
Hello,

I am currently taking Brief Calculus class and it's been a while since algebra for me. I am working on a homework problem and I need to create an equation. I fear the only way to make sure that we both understand what I need help on is to write out the entire text of the problem so you will be looking at the same information as me. So here goes;

Company Revenue
In its 2001 annual Report, the Coca Cola Company reported that "Our worldwide unit case volume increased 4 percent in 2001, on top of a 4 percent increase in 2000. The increase in unit case volume reflects consistent performance across certain key operations despite difficult global economic conditions. Our business system sold 17.8 billion unit cases in 2001. A unit case is equivalent to 24 eight-ounce servings of finished beverage.

a) Find a model for the number of unit cases sold (s) as a function of (t), where t is the number of years since 1999.

OK....I understand that this is an exponential growth rate equation. I have an equation of s(t)=17.8(1.04)^t-2 In 1999 t=0, in 2001 t=2. The answer in the back of my book has an equation of s(t)=16.5(1.04)^t

What happened to the exponent of t-2?
Click to expand...

\(\displaystyle s(t) \, = \, 17.8\cdot 1.04^{t-2}\)

\(\displaystyle s(t) \, = \, 17.8\cdot 1.04 ^{-2}\cdot 1.04^{t}\)

\(\displaystyle s(t) \, = \, 16.5 \cdot 1.04^{t}\)
 
Re: Derivative Applications

I see what you have done. My question is why is the t not connected to the 2. Are you just factoring? Thanks.
 
Re: Derivative Applications

I do not understand your question.

I am applying law of exponentiation that says

\(\displaystyle a^{(m-n)} \, = \, a^m \cdot a^{-n}\)

so

\(\displaystyle 1.04^{(t-2)} \, = \, 1.04^t \cdot 1.04^{-2}\)
 
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