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anonymous
 one year ago
Given the function \(f(x) = 5^x\), Section A goes from \(x = 0\) to \(x = 1\). Section B goes from \(x = 2\) to \(x = 3\).
Part A: Find the average rate of change for each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
anonymous
 one year ago
Given the function \(f(x) = 5^x\), Section A goes from \(x = 0\) to \(x = 1\). Section B goes from \(x = 2\) to \(x = 3\). Part A: Find the average rate of change for each section. Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.

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Excalibur0126
 one year ago
Best ResponseYou've already chosen the best response.0What's the question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not too sure how to do this @Excalibur0126

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5formula to find average rate of change (slope ) \[\huge\rm \frac{ y_2 y_1 }{ x_2 x_1 }\] given: x = 0 and x=1 substitute x for 0 and for 1 into \[\rm f(x)=5^x\]to find y `f(x) is same as y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00 is x^1? what is x^2 and y^2? @Nnesha

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5it's not x^2 (not squared) \[\huge\rm y_2\] means 2nd y you need two order pairs to find slope (x , y)(x,y) (0 , ?) ( 1,y) you should find y value when x = 0 so replace x with 0 \[\huge\rm f(0)=5^{0}\] f(0)= ??

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5exponent rule anything to the zero power is one \[\rm (anything)^0 = 1 ~~~(x)^0=1 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what are the steps to doing something like this in the simplest terms? @Nnesha

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5well first step) find y when x=0 , x=1 2nd step) find y when x=2 and x=3 when you get all y values then you can apply slope formula to find average rate of change

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5\[\huge\rm f(0)=5^0 ~~~~~~f(1)=5^1\] like i said f(x) is same as y so you replace f(0) and f(1) with y \[\large\rm y=5^0 ~~~~~~~~~~y=5^1\] simplify that^^ (0 , ?)( 1,?) when x=0 , y = ?? when x=1 y =what ? write your answer where i put the question marks

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea whats hapenning @Nnesha

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.55 to the zero power equal to what ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5no did you read my comments ^^??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0*1 (im kind of slow with math)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5yes right so when x=0 y = 1 (0 ,1) now replace x with 1 \[y=5^1\] 5^1 is same as 5 right so when x =1 y=5 (0 , 1)(1,5) two order pairs now you can use slope formula to find average rate of change

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats y2  y1 over x2  x1?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5yes right use these two points (0,1)(1,5)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.04 over 1 is the slope?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5perfect! that's average rate of change when x=0 and x=1 now

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5now find y when x=2 and x=3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(x=2 y=25) (x=3 y=125)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5nice now you can write answer for PART B

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait what was the answer for part A?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.5find average rate of change of `each` section average rate of change = `slope` we just found the answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its just the two slopes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay so For A should I write 4 over 1 and 100 over 1?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.52/1 is same as 2 so 4/1 is same as 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i write 4 and 100?
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