The following table represents an exponential function.

the exponential function represented by the table can be written in the form y=ab^x. find the values for a and b

a = 4

b = 1/2

Step-by-step explanation:

if x =0 then b^0 = 1. You have your first constant.

y = a*b^0

4 = a * 1

a = 4

Now you can pick 1 point to figure out b

x = 1

y = 2

y = a*b^x

2 = 4*b^1 but b^1 is just b

2 = 4* b

b = 2/4

b = 1/2

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true