To graph the line we need two points; we already have one the point (4,2) now we need to find another one; to do this we get the equation of the line given by:
where m is the slope and (x1,y1) are a point throught the line. Plugging the values given we have:
Now we give a value to x and find the corresponding y. If x=0, then:
hence we have the point (0,-2).
Now that we have two points (0,-2) and (4,2) we graph them on the plane and join them with a straight line, hence the graph is:
Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
Answer:
or
.
Step-by-step explanation:
We have been given that Nigel is planning his training schedule for a marathon over a 4-day period. He is uncertain how many miles he will run on two days. One expression for the total miles he will run is .
The Commutative Property of Addition states that we can add numbers in any order. For example a and b be two numbers.
According to Commutative Property of Addition .
Similarly, we can write an equivalent expression to our given expression as:
We can simplify our expression as:
.
Therefore, our required expression would be or
.