Find an exponential function of the form f(x) = ba given that the Y-intercept of the function is and the graph of the 5 (-1,– 3) e function passes through the point . Simplify your answer completely and enter exact answers only (no approximations). - - f(x) =

Find an exponential function of the form f(x) = ba given that the Y-intercept of the function is and the graph of the 5 (-1,– 3) e function passes through the point . Simplify your answer completely and enter exact answers only (no approximations). - - f(x) =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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Question

1
Find an exponential function of the form f(x)
= ba*
, given that the y-intercept of the function is -
and the graph of the
5'
(-1,-3)
e
function passes through the point
Simplify your answer completely and enter exact answers only (no approximations).
f(x) =

Expert Solution

Step 1

To find the y-intercept of the given function, substitute x=0

Then y-intercept is ba⁰=b

But given y-intercept of the function is -1/5

So b=-1/5

Given the graph of function is passing through the point (-1, -e/5)

That is -e/5=ba^-1=(-1/5)a^-1

Then a=1/e

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