C. StartFraction Natural Log of left-parenthesis 2208 right-parenthesis EndLog over 5 EndFraction
To find the value of the growth constant k, we can use the formula:
276,000 = 125 * e^(kt)
First, find the value of n by dividing the final amount by the initial quantity:
n = 276,000 / 125 = 2208
Therefore, the formula becomes:
276,000 = 125 * e^(k * 5)
Now, solve for k:
e^(5k) = 276,000 / 125
e^(5k) = 2208
5k = ln(2208)
k = ln(2208) / 5
Therefore, the value of the growth constant k is StartFraction Natural Log of left-parenthesis 2208 right-parenthesis EndLog over 5 EndFraction.
Use the given exponential growth formula to answer the question.
Information
y equals n e Superscript k t Baseline
Where n is the initial quantity,
t is the time,
k is the growth constant, and
y is the final amount.
Question
A new type of bacteria is found that grows exponentially. Scientists start with 125 bacteria in a sample colony. Five
days later there are 276,000 bacteria.
What is the value of the growth constant k?
Answer options with 4 options
A.
StartFraction 276000 over natural log of left-parenthesis 625 right-parenthesis EndLog EndFraction
B.
276000 natural log of left-parenthesis 625 right-parenthesis EndLog
C.
StartFraction Natural Log of left-parenthesis 2208 right-parenthesis EndLog over 5 EndFraction
D.
5 Natural Log of 2208 EndLog
1 answer