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

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.