Write the equation for a line that has an initial

Ответ:

animelover730

05.02.2022

Mathematics

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

initial value of 3, namely when x = 0, y = 3, so we have the point (0 , 3) and it has a rate or slope of 3/4.

$(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{3}{4}}(x-\stackrel{x_1}{0})\implies y=\cfrac{3}{4}x+3$

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Ответ:

jjjoooorrrrddddaannn

10.11.2022

Mathematics

Part A) A reasonable domain is the interval [0,8] $0\leq m\leq 8$

Part B) At the beginning of the study the length of the fish was 3 cm (see the explanation)

Part C) The average rate of change is 0.40\ cm/month (see the explanation)

Step-by-step explanation:

Let

m ---> the number of months

f(m) ---> the length of the fish in cm

we have

f(m)=3(1.09^m)

This is a exponential function of the form

f(m)=a(b^m)

where

a is the initial value or y-intercept

b is the base of the exponential function

b=1+r

r is the percent average of change

In this problem we have

$a=3\ cm\\b=1.09\\r=1.09-1=0.09\\r=0.09*100=9\%$

Part A) When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function?

For f(m)=5.98 cm

substitute the given value in the function

5.98=3(1.09^m)