Question

The exponential function
f
(
x
)
is represented by the equation
f
(
x
)
=
3
(
10
)
x
−
300
.

The linear function
g
(
x
)
has a slope of
2
and goes through the point
(
0
,
−
300
)
.



Which statement is TRUE about the intercepts of
f
(
x
)
and
g
(
x
)
?



A.
x
-intercept of
f
(
x
)
>
g
(
x
)

y
-intercepts are the same

B.
x
-intercept of
f
(
x
)
<
g
(
x
)

y
-intercepts are the same

C.
x
-intercept of
f
(
x
)
>
g
(
x
)

y
-intercept of
f
(
x
)
<
g
(
x
)

D.
x
-intercept of
f
(
x
)
<
g
(
x
)

y
-intercept of
f
(
x
)
>
g
(
x
)

Answer 1

Find the intercepts:

y-intercepts:
- f(0) = 3·10^0 − 300 = 3 − 300 = −297
- g(0) = −300
So f's y-intercept (−297) is greater than g's (−300).

x-intercepts:
- For g: 2x − 300 = 0 → x = 150
- For f: 3·10^x − 300 = 0 → 10^x = 100 → x = 2

So f's x-intercept (2) is less than g's (150).

Therefore statement D is true.