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).

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

i would say c is the best answer, hope it's right!

good luck! =)

cutie~

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841