Answer:
To find the total number of molds the company will manufacture over 10 weeks, we can use the formula for the sum of a geometric series:
\[ S = a \left( \frac{1 - r^n}{1 - r} \right) \]
Where:
- \( S \) is the total number of molds over 10 weeks.
- \( a \) is the initial number of molds (20,150 in this case).
- \( r \) is the common ratio (decrease of 2% each week, so \( r = 1 - 0.02 = 0.98 \)).
- \( n \) is the number of weeks (10 weeks).
Plugging in the values:
\[ S = 20150 \left( \frac{1 - 0.98^{10}}{1 - 0.98} \right) \]
\[ S = 20150 \left( \frac{1 - 0.817032}{0.02} \right) \]
\[ S = 20150 \left( \frac{0.182968}{0.02} \right) \]
\[ S = 20150 \times 9.1484 \]
\[ S = 184,218 \]
So, the company will manufacture approximately 184,218 molds during the 10-week period.