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.If there are 180180 grams of radioactive material with a half-life (decrease by half or 50%50%) of 11 hour, how much of the radioactive material will be left after 33 hours?y=𝑦= Answer 1 Question 17 (( Answer 2 Question 17 )x)𝑥What number will you fill in for x𝑥 to solve the equation? Answer 3 Question 17y=𝑦= Answer 4 Question 17CheckQuestion 17
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.If there are 180180 grams of radioactive material with a half-life (decrease by half or 50%50%) of 11 hour, how much of the radioactive material will be left after 33 hours?y=𝑦= Answer 1 Question 17 (( Answer 2 Question 17 )x)𝑥What number will you fill in for x𝑥 to solve the equation? Answer 3 Question 17y=𝑦= Answer 4 Question 17CheckQuestion 17
Solution
The equation for an exponential function with a half-life of 1 hour is y = 180 * (1/2)^x, where x is the number of hours and y is the amount of radioactive material left.
To find out how much of the radioactive material will be left after 3 hours, we substitute x with 3 in the equation:
y = 180 * (1/2)^3 = 180 * 1/8 = 22.5 grams.
So, after 3 hours, there will be 22.5 grams of the radioactive material left.
For the given question, the answers would be:
Answer 1 Question 17: 180 Answer 2 Question 17: 1/2 Answer 3 Question 17: 3 Answer 4 Question 17: 22.5
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