Question
Write an exponential function in the form
that goes through the points
and
.
Ask by Burgess Bartlett. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The exponential function is
.
Solution
To find an exponential function of the form
that passes through the points
and
, follow these steps:
-
Determine the value of
: When: Given thatwhen , we have: -
Determine the value of
: Using the point: Solve for: Take the cube root of both sides: -
Write the exponential function:Substituting
and into the general form:
Final Answer:
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Mind Expander
To find the exponential function
that passes through the points
and
, we can start by identifying
and
.
-
From the point
, we can say: So, we have. -
Next, use the point
: Dividing both sides by 20, we get:Taking the cube root of both sides:
Now, substituting
and
back into the original function gives us:
So the exponential function is: