In a lab experiment, a population of 500 bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after 4 hours? B=500(1+3)^(4) B=3(500)^(4) B=3(1+500)^(4) B=500(3)(3)(3)(3)

Question

In a lab experiment, a population of 500 bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after 4 hours?  B=500(1+3)^(4)  B=3(500)^(4)  B=3(1+500)^(4)  B=500(3)(3)(3)(3)

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We are given an initial population of bacteria, which is 500. We are told that this population triples every hour. We need to find the equation that represents the number of bacteria after 4 hours.Determine the growth pattern: Determine the growth pattern. Since the population triples every hour, the growth pattern is exponential. The number of bacteria after each hour can be found by multiplying the previous hour's population by 3.Write the equation: Write the equation for the exponential growth. The general formula for exponential growth is P(t) = P0 * r^t, where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in hours. In this case, P0 is 500, r is 3 (since the population triples), and t is 4 hours.Plug in values: Plug in the values into the exponential growth formula. Using the formula from Step 3, we get P(4) = 500 * 3^4. This represents the population after 4 hours.Simplify the equation: Simplify the equation. The equation simplifies to B = 500 * 3^4, which is the same as B = 500 * (3 * 3 * 3 * 3).

In a lab experiment, a population of $500$ bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after $4$ hours? $\newline$ $B=500(1+3)^{4}$ $\newline$ $B=3(500)^{4}$ $\newline$ $B=3(1+500)^{4}$ $\newline$ $B=500(3)(3)(3)(3)$

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