Question

In an exponential function f(x)=a(b)^x it is known that f(5)=15 and f(7)=170. Which of the following is the closest to the value of ;?

Answer 1

Complete question is;

In an exponential function, f(x) = a(b)^x, it is known that f(5) = 15 and f(7) = 170. which of the following is closest to the value of b?

Answer:

b = 3.37

Step-by-step explanation:

The function given is f(x) = a(b)^x,

Now, f(5) = 15, Thus;

15 = a(b)^(5)

Also, f(7) = 170

Thus; 170 = a(b)^(7)

From first equation, a = 15/(b)^(5))

Putting this in second equation;

170 = (15/(b)^(5))) × (b)^(7)

170 = 15b²

b² = 170/15

b² = 11.333

b = √11.333

b = 3.37