Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Given:
For en exponential function f(a):
[tex]f(-3)=18[/tex]
[tex]f(1)=59[/tex]
To find:
The value of f(0).
Solution:
The general form of an exponential function is:
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/ decay factor.
We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).
[tex]18=ab^{-3}[/tex] ...(ii)
We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).
[tex]59=ab^{1}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]
[tex]3.278=b^{1-(-3)}[/tex]
[tex]3.278=b^{4}[/tex]
[tex](3.278)^{\frac{1}{4}}=b[/tex]
[tex]1.346=b[/tex]
Substituting the value of b in (iii).
[tex]59=a(1.346)^1[/tex]
[tex]\dfrac{59}{1.346}=a[/tex]
[tex]43.83358=a[/tex]
[tex]a\approx 43.83[/tex]
The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].
Therefore, the value of f(0) is 43.83.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
