The formula \( \mathrm{S}=\mathrm{C}(1+r)^{t} \) models inflation, where \( \mathrm{C}= \) the value today, \( \mathrm{r}= \) the annual inflation rate (in decimal form), and \( \mathrm{S}= \) the inflated value tyears from now. If the inflation rate is \( 2 \% \), how much will a house now worth \( \$ 129,000 \) be worth in 16 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 a percentage to a decimal. So, \( r = 0.02 \). Next, substituting the values into the formula: \[ S = 129,000(1 + 0.02)^{16} \] \[ S = 129,000(1.02)^{16} \] Calculating \( (1.02)^{16} \) gives approximately \( 1.3728 \). Thus, we have: \[ S \approx 129,000 \times 1.3728 \approx 176,000.32 \] Rounding to the nearest dollar, the house will be worth \( \$ 176,000 \). The house will be worth \( \$ 176,000 \).