Chip Sales The worldwide sales of flash memory chips (in billions of dollars) is approximated by
S(t) = 4.3(t + 2)0.94     (0 ≤ t ≤ 6)
where t is measured in years, with t = 0 corresponding to 2002. Flash chips are used in cell phones, digital cameras, and other products.†
(a)
What were the worldwide flash memory chip sales in 2002, in billions of dollars? (Round your answer to two decimal places.)
$ 
 billion
(b)
What were the estimated sales for 2007, in billions of dollars? (Round your answer to two decimal places.)
$ 
 billion

We are given the function that models the worldwide sales of flash memory chips:

\[
S(t) = 4.3(t + 2)^{0.94}
\]

where $ t $ is the number of years after 2002.

### Part (a): Flash memory chip sales in 2002
In 2002, $ t = 0 $. To find the sales for that year, substitute $ t = 0 $ into the equation:

\[
S(0) = 4.3(0 + 2)^{0.94}
\]

### Part (b): Estimated sales for 2007
In 2007, $ t = 5 $ (since $ t = 0 $ corresponds to 2002, 2007 is 5 years later). To find the sales for 2007, substitute $ t = 5 $ into the equation:

\[
S(5) = 4.3(5 + 2)^{0.94}
\]

Let's calculate both values.### Part (a): The worldwide flash memory chip sales in 2002 were approximately **$8.25 billion**.

### Part (b): The estimated sales for 2007 were approximately **$26.78 billion**.

Would you like further details or clarifications on this problem? 

Here are 5 related questions to consider:
1. How would the sales in 2003 compare to those in 2002 based on the function?
2. What is the percentage increase in sales from 2002 to 2007?
3. What would the sales have been in 2005?
4. How does the rate of increase in sales change over the years?
5. Could this model predict sales beyond 2007, and if so, how reliable might it be?

**Tip:** In exponential-like models, the rate of growth can often be analyzed by differentiating the function to study how sales accelerate over time.

The worldwide sales of flash memory chips (in billions of dollars) is approximated by S(t) = 4.3(t + 2)^0.94 (0 ≤ t ≤ 6) where t is measured in years, with t = 0 corresponding to 2002. Flash chips are used in cell phones, digital cameras, and other products. (a) What were the worldwide flash memory chip sales in 2002, in billions of dollars? (b) What were the estimated sales for 2007, in billions of dollars?

This problem explores how to estimate worldwide sales of flash memory chips using the exponential model S(t) = 4.3(t + 2)^0.94, with t representing the number of years after 2002. Learn how to calculate sales for 2002 and 2007, and understand key algebraic concepts and real-world applications. Suitable for Grades 10-12.

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