\[ P(t) = P_0 e^{kt}, \]
![\[ P(t) = P_0 e^{kt}, \]](https://soloferat.biz.id/images/pt--p0-ekt-.jpg)
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- \[\boxed{\frac{v_0^2 \sin(2\theta)}{2g}}.\]
- A deep-sea extremophile genomics researcher is studying the growth dynamics of microbial communities near hydrothermal vents. The population of a certain microbial species is modeled by the equation \( P(t) = P_0 e^{kt} \), where \( k \) is a growth constant. If the population triples in 5 hours, what is the value of \( k \)?
- We are given the population model
- and that the population triples in 5 hours, so
- \[ P(5) = 3P_0. \]
- Substitute into the equation:
