\( 1< \) Use the simple interest formula to determine the missing value. \[ p=\$ 964.63, t=2.5 \%, t=?, i=\$ 48.23 \] \( t=\square \) years (Do not round until the final answer. Then round to the nearest whole number as needed.)

To find the missing value of time \( t \) in the simple interest formula, we start with the formula for simple interest: \[ i = p \times r \times t \] Where \( i \) is the interest earned, \( p \) is the principal amount, \( r \) is the rate (as a decimal), and \( t \) is the time in years. First, we convert the interest rate from percentage to a decimal: \( 2.5\% = 0.025 \). Now we can rearrange the formula to solve for \( t \): \[ t = \frac{i}{p \times r} \] Plugging in the known values: \[ t = \frac{48.23}{964.63 \times 0.025} \] Calculate it step-by-step: 1. Calculate \( 964.63 \times 0.025 = 24.11575 \). 2. Now divide: \( t = \frac{48.23}{24.11575} \approx 2.0 \). Thus, rounding to the nearest whole number, \( t = 2 \) years.