Which exponential equation contains the points (0,16)

Question

(
0
,
16
)
and (1,6.4)
(
1
,
6.4
)
?(1 point)
Responses

y=6.4x
𝑦
=
6.4
𝑥
y is equal to 6 point 4 to the x th power

y=16⋅6.4x
𝑦
=
16
⋅
6.4
𝑥
y is equal to 16 times 6 point 4 to the x th power

y=−16⋅0.4x
𝑦
=
−
16
⋅
0.4
𝑥
y is equal to negative 16 times 0 point 4 to the x th power

y=16⋅0.4x

Answer 1

To find the exponential equation containing the points (0, 16) and (1, 6.4), we can start with the general form of an exponential equation:

\[ y = a \cdot b^x \]

where \( a \) is the initial value (when \( x = 0 \)) and \( b \) is the base that determines the growth or decay factor.

Given the point (0, 16):

\[ y = a \cdot b^0 \] \[ 16 = a \cdot 1 \implies a = 16 \]

Now, using the point (1, 6.4):

\[ y = 16 \cdot b^1 \] \[ 6.4 = 16 \cdot b \] \[ b = \frac{6.4}{16} = 0.4 \]

Thus, the equation can be written as:

\[ y = 16 \cdot (0.4)^x \]

From the provided options, the correct equation is:

\[ y = 16 \cdot 0.4^x \]

So, the answer is:

y = 16⋅0.4^x