Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Given:
f(x) is an exponential function.
[tex]f(-3.5)=25, f(6)=33[/tex]
To find:
The value of f(6.5).
Solution:
Let the exponential function is
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth factor.
We have, [tex]f(-3.5)=25[/tex]. So, put x=-3.5 and f(x)=25 in (i).
[tex]25=ab^{-3.5}[/tex] ...(ii)
We have, [tex]f(6)=33[/tex]. So, put x=6 and f(x)=33 in (i).
[tex]33=ab^{6}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{33}{25}=\dfrac{ab^{6}}{ab^{-3.5}}[/tex]
[tex]1.32=b^{9.5}[/tex]
[tex](1.32)^{\frac{1}{9.5}}=b[/tex]
[tex]1.0296556=b[/tex]
[tex]b\approx 1.03[/tex]
Putting b=1.03 in (iii), we get
[tex]33=a(1.03)^{6}[/tex]
[tex]33=a(1.194)[/tex]
[tex]\dfrac{33}{1.194}=a[/tex]
[tex]a\approx 27.63[/tex]
Putting a=27.63 and b=1.03 in (i), we get
[tex]f(x)=27.63(1.03)^x[/tex]
Therefore, the required exponential function is [tex]f(x)=27.63(1.03)^x[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
