You are conducting a biology experiment and begin with 5000000 cells, but some of those cells are dying each minute. The rate of death of the cells is modeled by the function \( A(t)=A_{0} \cdot e^{-.598 t} \), where \( A_{0} \) is the original number of cells, \( t \) is time in minutes, and \( A \) is the number of cells remaining after \( t \) minutes. How many cells remain after 5,10 , and 25 minutes? Round each answer to the nearest cell. There are Submit Question

To calculate the remaining number of cells at different time intervals, we can plug in the values of \( t \) (5, 10, and 25 minutes) into the formula \( A(t) = A_0 \cdot e^{-0.598 t} \) where \( A_0 = 5000000 \). 1. **After 5 minutes**: \[ A(5) = 5000000 \cdot e^{-0.598 \cdot 5} \approx 5000000 \cdot e^{-2.99} \approx 5000000 \cdot 0.0502 \approx 251000 \] 2. **After 10 minutes**: \[ A(10) = 5000000 \cdot e^{-0.598 \cdot 10} \approx 5000000 \cdot e^{-5.98} \approx 5000000 \cdot 0.0023 \approx 11500 \] 3. **After 25 minutes**: \[ A(25) = 5000000 \cdot e^{-0.598 \cdot 25} \approx 5000000 \cdot e^{-14.95} \approx 5000000 \cdot 0.0000002 \approx 1 \] So rounding each answer to the nearest cell, we have approximately: - After 5 minutes: 251,000 cells - After 10 minutes: 11,500 cells - After 25 minutes: 1 cell You can see just how dramatically those cells diminish over time! It’s like a race against the clock with biology as the referee!