To find the constant of proportionality \( k \) when exchanging US Dollars (USD) for Philippine Pesos (PHP), we start with the relationship given by:
\[ \text{PHP} = k \cdot \text{USD} \]
From the information provided, we know that 950 USD can be converted into 39,687.20 PHP. Therefore, we can set up the equation:
\[ 39,687.20 = k \cdot 950 \]
To find \( k \), we solve for it:
\[ k = \frac{39,687.20}{950} \]
Calculating this gives:
\[ k = 41.8402 \]
Rounding to three decimal places:
\[ k \approx 41.840 \]
Next, to find the amount in PHP when converting 1,100 USD, we use the value of \( k \) we just found:
\[ \text{PHP} = k \cdot \text{USD} = 41.840 \cdot 1,100 \]
Calculating this:
\[ \text{PHP} = 41.840 \cdot 1,100 = 46,024 \]
Rounding to two decimal places as requested gives us:
\[ \text{PHP} \approx 46,024.00 \]
The final answers are:
- \( k = 41.840 \)
- Amount in PHP for 1,100 USD is \( 46,024.00 \) PHP.