Suppose that a new manufacturing company that makes plastic molds made 20,150 molds the first week. The company overestimated its requirements, and management intends to decrease the number of molds the company will manufacture by 2% each week for 10 wk. The number of molds that the company will make can be represented by a geometric sequence How many molds will the company manufacture during the 10 wk period? Round your answer to the nearest whole unit.​



Answer :

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.