Suppose that the exponential growth function is y = 4^x.
If x = 1, then y = 4^1 = 4.
If x = 3, then y = 4^3 = 64.
Let the initial value be 1/2.
The growth function is now y = 1/2 * 4^x.
If x =1, then y = 2 which is half of the y value before adding the 1/2.
If x = 3, then y = 1/2 * 64 = 32.
Answer: 1/2
Answer:
Step-by-step explanation:
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1) Graph the corresponding equation \( x = 2 \); this will split the plane into two regions. One of the region represents the solution set.
2) Select a point situated in any of the two regions obtained and test the inequality. If the point selected is a solution, then all the region is the solution set. If the selected point is not a solution, then the other (second) region represents the solution set.
3) Test: In this example, let us for example select the point with coordinates (3 , 2) which is in the region to the right of the line x = 2. If you substitute x in the inequality \( x ≥ 2 \) by 3 it becomes \( 3 ≥ 2 \) which is a true statement and therefore (3 , 2) is a solution. Hence, we can conclude that the region to the right of the vertical line x = 2 is a solution set including the line itself which is shown as a solid line because of the inequality symbol \( ≥ \) contains the \( = \) symbol. The solution set is represented by the blue hash region in the graph below including the line x = 2.
