College Algebra

Question

Use the function f(x)=1.05^x to answer the following questions. Round your answers to two decimal places.

so i know this part is

evaluate f(6): f(6)=1.05⁽⁶⁾ = 1.34

but im stuck on this part of the question

Determine x when f(x)= 11 x=?

Answer 1

11 = 1.05 ^ x

log 11 over base 1 05

X = 49.15

Answer 2

To start, let's go back to the first part of the problem. It says f(x)= 1.05x, Find f(6). You are not raising 1.05 to the 6th power--instead, you are multiplying. So, f(6)= 1.05(6)....f(6)= 6.3

For the second part of the problem, if says to find x when f(x)=11. Remember that f(x) is just a fancy way of saying "y" (your dependent variable). So substitute 11 in for f(x) and solve for x.

So,

11= 1.05x (Divide both sides of the equation by 1.05)

x = 10.48 (rounded to nearest 2 decimal places)