Question 9 of 9 . Step 1 of 1 The total attendance at a contemporary art museum is modeled by the function $$ f(x)=13,221(1,049)^{x} $$. If the initial total attendance (that is, the total attendance when $$ x=0 $$ ) was measured January 1, 2013, what will the total attendance be on January 1,2029 ? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window)

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To find the total attendance at the contemporary art museum on January 1, 2029, we need to evaluate the function $$ f(x) = 13,221(1.049)^{x} $$ at the appropriate value of $$ x $$.

1. **Determine the value of $$ x $$**:
   - The function is modeled with $$ x = 0 $$ corresponding to January 1, 2013.
   - To find the value of $$ x $$ for January 1, 2029, we calculate the number of years from 2013 to 2029:
     $$
     x = 2029 - 2013 = 16
     $$

2. **Substitute $$ x $$ into the function**:
   - Now we substitute $$ x = 16 $$ into the function:
     $$
     f(16) = 13,221(1.049)^{16}
     $$

3. **Calculate $$ f(16) $$**:
   - We will calculate $$ (1.049)^{16} $$ first and then multiply by $$ 13,221 $$.

Let's perform the calculation.
Calculate the value by following steps:
- step0: Calculate:
  $$13221\times 1.049^{16}$$
- step1: Convert the expressions:
  $$13221\left(\frac{1049}{1000}\right)^{16}$$
- step2: Simplify:
  $$13221\times \frac{1049^{16}}{1000^{16}}$$
- step3: Multiply:
  $$\frac{13221\times 1049^{16}}{1000^{16}}$$
The calculation gives us:

$$
f(16) \approx 28,423.144065
$$

Rounding this to the nearest whole number, the total attendance at the contemporary art museum on January 1, 2029, will be approximately:

$$
\boxed{28423}
$$
The total attendance on January 1, 2029, will be approximately 28,423.

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