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.