https://file.aiquickdraw.com/mathbot/file/1726085484734bkh5nebk.jpg

To solve the problems, let's use the formula provided:

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

where \( S(t) \) represents the worldwide sales of flash memory chips in billions of dollars and \( t \) is the number of years since 2002.

### Part (a)
We want to find the sales in 2002. Since \( t = 0 \) corresponds to 2002, we substitute \( t = 0 \) into the formula:

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

Let's calculate \( S(0) \):

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

### Part (b)
For the year 2005, \( t = 3 \) because 2005 is 3 years after 2002. Substitute \( t = 3 \) into the formula:

\[
S(3) = 4.3(3 + 2)^{0.94}
\]

Let's calculate both values now.The calculated values for the worldwide flash memory chip sales are:

### (a) For the year 2002:
\[
S(0) \approx 8.25 \text{ billion dollars}
\]

### (b) For the year 2005:
\[
S(3) \approx 19.52 \text{ billion dollars}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would the sales change if the exponent was different, such as \(0.85\) instead of \(0.94\)?
2. What would the sales be in 2007 (5 years after 2002)?
3. How does changing the base value of 4.3 affect the sales over time?
4. Can we derive a year when the sales would exceed 30 billion dollars?
5. How would you model the sales if the growth was exponential instead of a power function?

**Tip:** When working with functions, always substitute values carefully and check the units to ensure the answers make sense in context.

The worldwide sales of flash memory chips (in billions of dollars) is approximated by S(t) = 4.3(t + 2)^0.94, where t is measured in years. Find (a) the worldwide sales in 2002 (t = 0) and (b) the estimated sales for 2005 (t = 3).

This problem involves calculating the worldwide sales of flash memory chips using the power function formula S(t) = 4.3(t + 2)^0.94. Learn how to compute the sales for 2002 (t = 0) and estimate the sales for 2005 (t = 3). This is suitable for students in Grades 10-12.

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