Instructions: Create the equation of the form y=a(b)x for the exponential function described in each real-world problem. Then, use the equation to answer the question.The number of bacteria in a petri dish on the first day was 113113 cells. If the number of bacteria increase at a rate of 82%82% per day, how many bacteria cells will there be after 77 days?y=𝑦= Answer 1 Question 16 (( Answer 2 Question 16 )x)𝑥What number will you fill in for x𝑥 to solve the equation? Answer 3 Question 16y=𝑦= Answer 4 Question 16
Question
Instructions: Create the equation of the form y=a(b)x for the exponential function described in each real-world problem. Then, use the equation to answer the question.The number of bacteria in a petri dish on the first day was 113113 cells. If the number of bacteria increase at a rate of 82%82% per day, how many bacteria cells will there be after 77 days?y=𝑦= Answer 1 Question 16 (( Answer 2 Question 16 )x)𝑥What number will you fill in for x𝑥 to solve the equation? Answer 3 Question 16y=𝑦= Answer 4 Question 16
Solution
The equation for the exponential function in this problem is y = a(b)^x, where:
- y is the number of bacteria cells
- a is the initial number of bacteria cells
- b is the rate of increase
- x is the number of days
Given in the problem, a = 113113 and b = 1 + 82/100 = 1.82 (since the rate of increase is 82%).
So, the equation becomes y = 113113(1.82)^x.
To find the number of bacteria cells after 77 days, we fill in x = 77 in the equation.
So, y = 113113(1.82)^77.
This is the equation you would solve to find the number of bacteria cells after 77 days.
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