A scatter plot is made with the data shown. Number of Bakers at a 5 5 6 7 8 9 10 11 12 13 Cake Shop Number of Cakes 7 7 8 89 11
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Answer: There were 1,250 bacteria present initially.
Step-by-step explanation:
To find the exponential growth to this, lets create an exponential model shown as below:
f(x) = a()
Let y represent the amount of hours have passed after the third-hour recording. With the information given, we can create a set of input-output pairs: (0 , 10000) and (2 , 40000). Now that we have this set of pairs, we have given ourselves the initial value of the function, a = 10,000. We can now substitute the second point into the equation using N = 40,000.
N(y) = 10000b^y
40000 = 10000b^2 Divide and write in lowest terms.
÷10000 ÷10000
4 = b^2
b = Isolate b using properties of exponents.
b = 2
Now that we have the exponential growth, we can use b = 2 to work backwards and find the initial amount of bacteria.
10,000 ÷ 2 = 5,000 <-- Amount of bacteria 2nd hour
5,000 ÷ 2 = 2,500 <-- Amount of bacteria 1st hour
2,500 ÷ 2 = 1,250 <-- Initial amount of bacteria.
The initial amount of bacteria is 1,250