Exponential equation. Picture is attached.

Question

asked Feb 19, 2021 23.0k views

1 Answer

Astrit Veliu · Answer 1 · 2021-02-23T18:45:55+0000

Answer:

y=106.656*(0.816)^x

Explanation:

The exponential equation will be of the form:

y=ba^x.

Now from the information give we have two points:

at
x=3,
y=58.

at
x=10,
y=14.

Thus we have two equations

(1).58=ba^3,

(2).14=ba^(10).

From equation
(1) we solve for
:

b=(58)/(a^3),

and put this value into equation
(2) and we get:

14=(58)/(a^3)*a^(10)=58a^7,

and solve for

$a=\sqrt[7]{(14)/(58) }=0.8162.$

$\boxed{a=0.816.}$

We now put this value into equation (1) and solve for
:

$\boxed{b=(58)/((0.8162)^3) =106.656.}$ .

With values of
and
in hand, we have our exponential function:

$\boxed{y=106.656*(0.816)^x.}$