The formula \( \mathrm{S}=\mathrm{C}(1+r)^{\mathrm{t}} \) models inflation, where \( \mathrm{C}= \) the value today, \( \mathrm{r}= \) the annual inflation rate (in decimal form), and \( \mathrm{S}= \) the inflated value \( t \) years from now. If the inflation rate is \( 5 \% \), how much will a house now worth \( \$ 177,000 \) be worth in 10 years? Round your answer to the nearest dollar. The house will be worth \( \$ \square \). (Round to the nearest dollar as needed.)

To find the future value of the house using the formula \( S = C(1 + r)^t \), we first convert the inflation rate from percentage to decimal form. The inflation rate \( r = 5\% = 0.05 \). We plug the values into the formula with \( C = 177,000 \) and \( t = 10 \): \[ S = 177,000 \times (1 + 0.05)^{10} \] Calculating this gives: \[ S = 177,000 \times (1.05)^{10} \approx 177,000 \times 1.62889 \approx 288,330.93 \] Rounding to the nearest dollar, the house will be worth \( \$288,331 \). So, the house will be worth \( \$288,331 \).