Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The normal exponential function is in form

$y = ab {}^{x}$

let plug in 0,8

$8 = ab {}^{0}$

b^0=1

so

$8 = a \times 1 = \: \: \: \: a = 8$

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

$25 = b {}^{2}$

$\sqrt{25}$

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

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

Answer 2

Answer:

$y=8(5)^x$

Step-by-step 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:

$y=8(5)^x$