created question points Points: 0 of 1 Save The government, through a subsidy program, distributes $\$ 23,000,000$. If each person or agency spends $45 \%$ of what is received, and $45 \%$ of this is spent, and so on, how much total increase in spending results from this goverment action? (Let $\mathrm{a}_{1}=10,350,000$ ) The total increase in spending will be approximately $\$ \square$. (Round to the nearest dollar as needed)
Solution
Step 1 ：The government, through a subsidy program, distributes $23,000,000.
Step 2 ：Each person or agency spends 45% of what is received, and 45% of this is spent, and so on.
Step 3 ：This forms a geometric series where the first term (a) is $0.45 * 23,000,000$ and the common ratio (r) is $0.45$.
Step 4 ：We can find the total increase in spending by using the formula for the sum of an infinite geometric series, $S = a / (1 - r)$.
Step 5 ：Substituting the values, we get $S = 10350000.0 / (1 - 0.45)$.
Step 6 ：Solving this gives us $S = 18818181.818181816$.
Step 7 ：Rounding to the nearest dollar, the total increase in spending will be approximately $18,818,182$.
Step 8 ：Final Answer: The total increase in spending will be approximately $\boxed{18,818,182}$.
