Write an exponential equation in the form y=ab^x whose graph passes through points (-3,24) and (-2,12).

The values to satisfy this equation would be a = 3 and b = .5.

In order to solve this we must first look at the equation with the second ordered pair in it. We can then solve for a.

y = ab^x

12 = ab^-2

12 =

12b^2 = a

Now that we have this solved for a, we can place that value in for a using the first ordered pair's values.

y = ab^x

24 = ab^-3

24 = 12b^2b^-3

24 = 12b^-1

24 =

24b = 12

b = .5

Now that we have the value of b, we can use either ordered pair and the b value to find a.

y = ab^x

12 = a(.5)^-2

12 = a(4)

a = 3

24b

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500