A culture of yeast cells grows exponentially with a rate constant of $0.5{\text{hr}}^{-1}$. If the initial cell count is $2\times 10^4$, how many cells will be present after $6$ hours?

Step-by-step solution

1. Write the exponential growth formula $N(t)=N_0{e}^{rt}$.
2. Substitute $N_0=2\times 10^4$, $r=0.5{\text{hr}}^{-1}$, and $t=6\text{hr}$: $N(6)=2\times 10^4,e^{0.5\times 6}$.
3. Calculate the exponent: $0.5\times 6=3$. So $N(6)=2\times 10^4,e^3$.
4. Use the value $e^{3}approx20.085$.
5. Multiply: $2\times 10^4\times 20.085\approx 4.017\times 10^5$.
6. Round to one significant figure to get $4.0\times 10^5$ cells.

Concept tested: Exponential population growth

Published 19 September 2026 · How this solution was prepared and checked