Question

Help me solve my math

Answer 1

653.3 bacteria

Explanation:

A continuously growing population of bacteria is modeled by the function:

`P(t) = P_0 \cdot e^(rt)`

where:

• 
  `P(t)` is the population after
  `t` time periods
• 
  `P_0` is the initial population
• 
  `r` is the relative rate of growth

In this problem, we are given the following values:

• 
  `P_0 = 484 \text{ bacteria}`
• 
  `r = 15\% = 0.15`
• 
  `t = 2`

We can plug these into the function to solve for
`P(2)`.

`P(t) = P_0 \cdot e^(rt)`

`P(2) = 484 \cdot e^((0.15 \, \cdot \, 2))`

`P(2) = 484 \cdot e^(0.3)`

Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.

`\huge{\text{P(2) = 653.3 bacteria}}`