Question

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (3, StartFraction 108 Over 5 EndFraction), (2, 36), (1, 60), (0, 100). Which function represents the given graph? f(x) = 100 · (Three-fifths)x f(x) = (100 · Three-fifths)x f(x) = 100 + Three-fifthsx f(x) = 100 · (Two-fifths)x

Answer 1

the correct answer is A

Explanation:

Answer 2

`f(x)=100((3)/(5) )^x`

Explanation:

Since the exponential function approaches y=0, its equation is of the form,

`f(x)=a(b^x)`

The point (0,100) is this graph so it must satisfy its equation

`100=a*b^0`

`100=a(1)`

a=100

The equation now becomes:

`f(x)=100*b^x`

We now substitute the point (1,60)

`60=100*b^1`

`b=(60)/(100) =(3)/(5)`

Therefore the required equation is
`f(x)=100((3)/(5) )^x`