The ordered pairs (2,100) and (3,1000) are solutions to an exponential equation. Write the equation.

Question

I need help with this please. Any help is appreciated. Thanks.

Answer 1

Start with knowing the general exponential growth formula y = ab^x where a = y-intercept and b is the "multiplier" (what's going on from one point to the other.)

x y

2, 100 you mulitply 100 by 10 to get the 1000 so your "b" is 100

3, 1000

Since you are multiplying going down the chart, you will divide by 10 to go up the chart until

you get to your y -intercept (where x = 0)

0, 1

1, 10

So your y intercept is 1 Equation is y = 1(10)^x

That was fun!

Jetta McGinniss

Answer 2

An exponential equation has the form y = A(B^x)

Since (2, 100) and (3,1000) are points on the graph, we get the following system of equations:

100 = A(B²) and 1000 = A(B³)

From the first equation, A = 100 / B²

Substitute for A in the other equation to get 1000 = (100/B²)B³

So, B = 10 and A = 100 / 10² = 1

Therefore, y = 10^x