PLZ ANSWER. I'M DOING HOMEWORK AT MIDNIGHT AND WANT TO SLEEP BUT I WANT THIS DONE FIRST

Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes​ f(x) =​ g(x).

​f: initial value of 400 decreasing at a rate of 14​%
​g: initial value of 30 increasing at a rate of 14​%

Write the exponential function for f.

f(x)=400(0.86)^x

Write the exponential function for g.

g(x) = 30(1.14)^x

The value of x that makes ​f(x) = g(x) is x= ___.
​(Round to the nearest integer as​ needed.)

(i messed up the formatting before so i need to ask it again, sorry).

Respuesta :

Answer: I think the answer is 9

Step-by-step explanation:

Ver imagen thebobhair

Answer:

9

Step-by-step explanation:

30×(1.14^x) = 400×(0.86^x)

400/30 = (1.14^x)/(0.86^x)

40/3 = [1.14/0.86]^x

Apply logs both sides with any base, I'm using log base 10 which is lg.

lg(40/3) = lg[1.14/0.86]^x

lg(40/3) = x × lg[1.14/0.86]

x = lg(40/3) ÷ lg[1.14/0.86]

x = 9.19

Nearest integer, x = 9