Question

Which exponential equation contains the points (−1,5)
(
−
1
,
5
)
and (2,5000)
(
2
,
5000
)
?(1 point)
Responses

y=(500)x
𝑦
=
(
500
)
𝑥
y is equal to 500 to the x th power

y=50⋅(10)x
𝑦
=
50
⋅
(
10
)
𝑥
y is equal to 50 times 10 to the x th power

y=50⋅−(10)x
𝑦
=
50
⋅
−
(
10
)
𝑥
y is equal to 50 times negative 10 to the x th power

y=−50⋅(10)x

Answer 1

To find the exponential equation that contains the points (-1, 5) and (2, 5000), we can start by trying the general form of an exponential equation, which can be written as:

\[ y = ab^{x} \]

where \( a \) and \( b \) are constants.

1. **Using the point (-1, 5)**:
\[
5 = ab^{-1}
\]
\[
5 = \frac{a}{b}
\]
\[
a = 5b
\]

2. **Using the point (2, 5000)**:
\[
5000 = ab^{2}
\]
Substitute \( a \) in the equation:
\[
5000 = (5b)b^{2}
\]
\[
5000 = 5b^{3}
\]
\[
b^{3} = \frac{5000}{5} = 1000
\]
\[
b = 10
\]

3. **Now substitute \( b \) back to find \( a \)**:
\[
a = 5b = 5 \times 10 = 50
\]

Now we have:
\[
y = 50 \cdot 10^{x}
\]

Thus, the correct exponential equation containing the points (-1, 5) and (2, 5000) is:

\[
y = 50 \cdot (10)^{x}
\]

This matches the second option you provided.