I need help in algebra 1. I have 4 questions, I already answered 3 of them, but I need help with the other
Andrew measures the amount of a very unstable substance to be 100 moles. The half-life of this substance is 3 days (after 3 days, half is gone).
1. Write an exponential function that models this situation where y is the amount of substance and x is time in days.
I think it's: y=100^.(1/2)^t/3
2. Use your equation from problem 1 to complete the chart:
Days Amount
-3 (3 days prior) 200
0 100
3 50
6 25
9 12.5
12 6.25
Did I fill in the chart correctly?
3. Use your data from problem 2 to graph your equation from problem 1
I'm not sure how to graph it :/
4. Calculate the expected amount of substance if Andrew had taken his measurements 9 days earlier. Show your calculations and consider the tend of your graph for problem 3
My answer:
x=-9
y=100^.(1/2)^-3
y=100^.(1/2)^-9/3
y=100^.(1/2)^-3=100^.8=800 moles
All help appreciated! Thanks!
1. yes y = 100 (1/2)^(t/3)
2. looks good, divide by 2 every three days
3. I can not very well show you a graph
maybe google
graph exponential
or graph A * B^-(kt)
4. 100 /(1/2)^3 = 100/(1/8) = 800
so yes but do not understand how you did it
Okay thank you so much Damon! :D
apparently her notation is ^. for * meaning multiply.
Trés strange.
Let's go through each question step by step:
1. To write an exponential function that models this situation, we need to use the formula:
y = initial amount * (1/2)^(t/h)
Where:
- y is the amount of substance
- t is the time in days
- initial amount is the starting amount of the substance
- h is the half-life of the substance
In this case, the initial amount is 100 moles and the half-life is 3 days. So the exponential function will be:
y = 100 * (1/2)^(t/3)
2. Let's fill in the chart using the equation obtained in problem 1:
Days Amount
-3 (3 days prior) 200
0 100
3 50
6 25
9 12.5
12 6.25
To calculate the amount for each day using the equation, substitute the value of t into the equation and solve for y. For example, for day -3 (3 days prior), substitute t = -3 into the equation:
y = 100 * (1/2)^(-3/3)
y = 100 * (1/2)^(-1)
y = 100 * (1/2)
y = 50
So the amount for day -3 is 50. Repeat this process for each day in the chart.
3. To graph the equation from problem 1, plot the points from the completed chart (question 2) on a graph and then connect them with a smooth curve. The x-axis represents time in days, and the y-axis represents the amount of substance. Each point represents a day and its corresponding amount. Connect the points with a smooth curve to represent the trend of the exponential function.
4. To calculate the expected amount if Andrew had taken his measurements 9 days earlier, we can use the same equation from problem 1:
y = 100 * (1/2)^(t/3)
Substitute t = -9 into the equation:
y = 100 * (1/2)^(-9/3)
y = 100 * (1/2)^(-3)
y = 100 * (1/8)
y = 800 moles
So the expected amount of substance if Andrew had taken his measurements 9 days earlier is 800 moles.
I hope this clarifies the process and helps you understand algebraic concepts better.