Pregunta
If
is an exponential function of the form of
where
and
,
then find the value of
, to the nearest hundredth.
then find the value of
Ask by Valdez Powers. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Solución
Given that
is an exponential function of the form
, where
and
, we need to find the value of
to the nearest hundredth.
To find the value of
, we first need to determine the values of
and
using the given information.
From the given information, we have:
We can use these two equations to solve for
and
.
Let’s start by using the first equation
to find the value of
:
Now, let’s use the second equation
to find the value of
:
We can solve these two equations simultaneously to find the values of
and
.
Let’s solve these equations to find the values of
and
and then use them to find the value of
.
Solve the system of equations by following steps:
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
- step1: Calculate:
- step2: Solve the equation:
- step3: Substitute the value of
- step4: Reduce the fraction:
- step5: Swap the sides:
- step6: Divide both sides:
- step7: Divide the numbers:
- step8: Raise both sides to the
-th power
- step9: Evaluate the power:
- step10: Substitute the value of
- step11: Simplify:
- step12: Calculate:
- step13: Check the solution:
- step14: Rewrite:
The solution to the system of equations isand .
Now that we have the values of
and
, we can find the value of
using the exponential function
.
Substitute the values of
and
into the function to find
:
Let’s calculate the value of
to the nearest hundredth.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Evaluate the power:
- step2: Rewrite the expression:
- step3: Reduce the numbers:
- step4: Multiply:
- step5: Evaluate the power:
The value ofto the nearest hundredth is 182.25.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Beyond the Answer
To solve for
, we start with the given form of the function
and the provided values
and
.
Setting up the equations with the known values:
-
From
: -
From
:
Next, we can express
in terms of
:
Substituting this into equation (2):
Now, replacing
from equation (1):
Solving for
:
To find
, we square both sides:
Now, substitute
back into equation (1) to find
:
Calculating
:
Then,
Now we can express
fully:
Finally, we need to find
:
Calculating
:
Then,
Thus, the value of
to the nearest hundredth is:

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