The table represents some points on the graph of an exponential function.
x -1 l 1 l 3 l 5l
k(x) 0.02 l 2 l 200 l 20,000l
Based on the table, which function represents the same relationship?
Option A.
K(x) = 0.2 (10)^x
Option B.
K(x) = 2(10)^x
Option C.
K(x) = 10(0.2)^x
Option D.
K(x) = 10(2)^x
The exponential function formula is given by K(x) = a(b)^x, where a is the initial value and b is the base.
Looking at the table, we can see that for x = -1, K(x) = 0.02, and for x = 1, K(x) = 2. This means that the base b is 10, because (10)^-1 = 0.1 and (10)^1 = 10.
Now, looking at the initial value, for x = -1, K(x) = 0.02. This means that a = 0.02.
So the exponential function that represents the same relationship as the table is K(x) = 0.02(10)^x. Comparing this to the options, we see that the correct answer is:
Option A.
K(x) = 0.2(10)^x
Which situation does NOT show causation?
{silence}Option A.{silence}
As the dimensions of a floor increase, the area of the floor also increases.
{silence}Option Be.{silence}
As the amount of dirt in a truck decreases, the total weight of the truck also decreases.
{silence}Option C.{silence}
As the number of hats sold at a baseball game increases, the number of runs scored by the home team also increases.
{silence}Option D.{silence}
As the number of grams of sugar in a beverage decreases, the number of calories in the beverage also decreases.
The situation that does NOT show causation is:
Option C.
As the number of hats sold at a baseball game increases, the number of runs scored by the home team also increases.
This is because there may be other factors, such as the skill level of the players or the quality of the opponent, that could also influence the number of runs scored by the home team. Just because the number of hats sold and the number of runs scored increase together does not mean that one directly causes the other.