Given the function f (x) = 630(.64)^x, determine if this

William Collins

William Collins

Answered question

2022-01-21

Given the function f(x)=630(.64)x, determine if this function models exponential growth or decay and identify the growth or decay rate.

Answer & Explanation

mauricio0815sh

mauricio0815sh

Beginner2022-01-21Added 34 answers

Given, 
f(x)=630(.64)x, 
We must recognize it as an exponential growth and decay function and determine the rate of growth or decay. 
We have 
f(x)=630(0.64)x 
In (0.64)x; 0.64<1 
So, 
As x is increasing then (0.64)x is decreasing ; in turn f(x)=630(0.64)x is decreasing 
So, 
f(x)=630(0.64)x is a exponential decay function 
Now, 
Decay rate =d(f(x)) dx  
Differentiating f(x)=630(0.64)x with respect to x 
d(f(x)) dx =630×ln(0.64)×(0.64)x (using d(ax) dx =axlna) 
d(f(x)) dx =630×(0.446)×(0.64)x 
Answer 
d(f(x)) dx =281.16(0.64)x

Donald Cheek

Donald Cheek

Beginner2022-01-22Added 41 answers

finally found!!!

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