A quantity with an initial value of 7200 decays exponentially at a rate of \( 0.3 \% \) every day. What is value of the quantity after 10 weeks, to the nearest hundredth?

To calculate the value of the quantity after 10 weeks, given an initial value of 7200 that decays at a rate of 0.3% per day, we can use the formula for exponential decay: \[ A = A_0 e^{-kt} \] Where: - \( A_0 = 7200 \) - \( k = 0.003 \) (the decay rate in decimal form) - \( t = 10 \text{ weeks} = 10 \times 7 = 70 \text{ days} \) Substituting the values into the formula gives us: \[ A = 7200 \times e^{-0.003 \times 70} \] Calculating the exponent: \[ 0.003 \times 70 = 0.21 \] Now we plug that back into the equation: \[ A = 7200 \times e^{-0.21} \] Calculating \( e^{-0.21} \): Approximately, \( e^{-0.21} \approx 0.809 \). Finally, multiplying: \[ A \approx 7200 \times 0.809 \approx 5824.80 \] The value of the quantity after 10 weeks is approximately **5824.80** to the nearest hundredth.