A Petri dish containing 500,000 bacteria is used in an experiment investigating growth rates for bacteria. The table below shows the number of bacteria, N(t), in the Petri dish after t minutes.
t N(t)
1 520,000
2 540,800
3 562,432
Select the equation that models N(t).
N(t)=500,000(1.04)tcap n times t is equal to 500 comma 000 1 point 0 4 to the t th power , ,
N(t)=520,000+1.04(t−1)cap n times t is equal to 520 comma 000 plus 1 point 0 4 raised to the open paren t minus 1 close paren power
N(t)=520,000(1.04)tcap n times t is equal to 520 comma 000 1 point 0 4 to the t th power , ,
N(t)=500,000(1.04)t−1
Well, it seems you're dealing with some bacteria party in a Petri dish! Let's find the equation that models the number of bacteria, N(t), after t minutes.
Looking at the options, the equation that makes the most sense is N(t) = 520,000 + 1.04(t - 1). This equation takes into account the initial number of bacteria (520,000) and the growth rate of 1.04.
So, it seems like those bacteria are multiplying and having a good time in that Petri dish!
The correct equation that models N(t) is:
N(t)=500,000(1.04)^t
To determine the equation that models N(t), we can analyze the given data points.
Let's start by looking at the initial value of N(1), which is 500,000 bacteria. This tells us that the base value in the equation should be 500,000.
Next, we need to consider how the number of bacteria changes over time. By observing the data points, we can see that the population is increasing, indicating a growth model.
Additionally, we notice that the population size appears to be increasing by a certain factor with each passing minute. In this case, the factor is 1.04.
With this information in mind, we can eliminate options that do not match these observations.
Option 1, N(t) = 500,000(1.04) to the power of t, could be a valid equation since it incorporates the base value of 500,000 and the growth factor of 1.04.
Option 2, N(t) = 520,000 + 1.04(t-1), does not match our observations of exponential growth. This equation includes a linear term (t-1) and does not represent exponential growth.
Option 3, N(t) = 520,000(1.04) to the power of t, matches the observations. It has the base value of 520,000, which is not consistent with the given initial value of 500,000.
Option 4, N(t) = 500,000(1.04) to the power of (t-1), does not match the given data points. The power of (t-1) suggests that the initial data point should be for t=0, which is inconsistent with the given data.
Therefore, the equation that models N(t) is N(t) = 500,000(1.04) to the power of t.
520/500 = 1.04
since N(1) = 500K * 1.04^1, it sure looks like
N(t) = 500K * 1.04^t
if you can match that with any of those horribly typed choices, go for it.