+152 Assume f is an exponential function with the two given values. Use the property of exponential functions to calculate values of f(x) for one larger value of x and for one smaller value of x. Then use the calculated and given points to plot the graph.
f(5)= 80, f(7)= 64, f(9) = 51.2, f(11) = 40.69
+128406 We have
80 = ab^5 → a = 80/b^5
And
64 = ab^7 → a = 64/b^7
Setting the "a's" equal, we have
80/b^5 = 64/b^7
b^2 = 64/80 = 4/5 = .8
b = √.8 = .894
And solving for "a" we have
80 = a(.894)^5
80 = a(.571)
a = 80/.571 = 140.1
So...our function is
f(x) = 140.1 (.894)^x
Here's a graph...https://www.desmos.com/calculator/uvldjauwxm
+128406 We have
80 = ab^5 → a = 80/b^5
And
64 = ab^7 → a = 64/b^7
Setting the "a's" equal, we have
80/b^5 = 64/b^7
b^2 = 64/80 = 4/5 = .8
b = √.8 = .894
And solving for "a" we have
80 = a(.894)^5
80 = a(.571)
a = 80/.571 = 140.1
So...our function is
f(x) = 140.1 (.894)^x
Here's a graph...https://www.desmos.com/calculator/uvldjauwxm
