Question

20 points! Write an exponential function in the form y=ab^x that goes through points (0, 8) and (2, 200)

Answer 1

`y = 8(5) {}^(x)`

Explanation:

The normal exponential function is in form

`y = ab {}^(x)`

let plug in 0,8

`8 = ab {}^(0)`

b^0=1

so

`8 = a * 1 = \: \: \: \: a = 8`

So so far our equation is

`y = 8b {}^(x)`

So now let plug in 2,200

`200 = 8b {}^(2)`

Divide 8 by both sides and we get

`25 = b {}^(2)`

`√(25)`

Which equal 5 so b equal 5. So our equation is

`y = 8(5) {}^(x)`

Answer 2

`y=8(5)^x`

Explanation:

We want an exponential function that goes through the two points (0, 8) and (2, 200).

Since a point is (0, 8), this means that y = 8 when x = 0. Therefore:

`8=a(b)^0`

Simplify:

`a=8`

So we now have:

`y = 8( b )^x`

Likewise, the point (2, 200) tells us that y = 200 when x = 2. Therefore:

`200=8(b)^2`

Solve for b. Dividing both sides by 8 yields:

`b^2=25`

Thus:

`b=5`

Hence, our exponential function is:

`y=8(5)^x`