3. Refer to R as given in Table 21. You may assume that R is continuous on the i
ID: 2912174 • Letter: 3
Question
3. Refer to R as given in Table 21. You may assume that R is continuous on the interval 0 Table 21: Table for R 3. 0 1 2 3 R() 6 24 96 384 (a) Assuming that R is an exponential function, find a function equation for R (b) Find the average rate of change of R on the interval 0 2 (c) Using the function equation for R, find the average rate of change of R on the interval 1 rs5. (d) Using the function equation for R, what is the range of R on the domain of all real numbers? (e) Using the function equation for R, write a function equation for the inverse, R-1 (f) Let U(x) R2r)-3. Describe how the graph of U will differ from the graph of R. Then verify your description using Desmos. (g) What is the range of U? (h) Let V(x) In(R(x)). Write a function equation for V.Explanation / Answer
Let the exponential function is
(a.) R(x)=t*(ax)
using the values given, at x=0,R(x)=6
putting the values we get,
6=t(a0), -> t=6;
using the 2nd value set , x=1,R(x)=24
24=6(a1)
a=24/6=4
so, R(x)=6(4x)
(b). average rate of change over the interval (0,2)
= (R(2)-R(0))/(2-0)
= (96-6)/(2-0)=45
(c) average rate of change over the interval (1,5)
= (R(5)-R(1))/(5-1)
=(6(45)-24)/(5-1)=1530
(d). As the function is exponential, so the value of R(x) is always positive the range of the function is (0,).
(e). Let y=6(4x)
y/6=4x , taking log to the base 4
x=log4(y/6)
the inverse is Y=log4(X/6)
(h). V(x)=ln(R(x))
=ln(6*(4x)), using the property of log
=ln(6)+ln(4x)
V(x)=ln(6)+xln(4)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.