Answer :
The average rate of change is 37.5.
Define Rate of change
- Rate of change (ROC) refers to how quickly something changes over time.
- The acceleration or deceleration of changes (i.e., the rate) and not the magnitude of individual changes themselves.
- Formula is, Rate of change = ( f(b) - f(a) ) / (b - a)
Given function is,
f(x) = 5(2) ^ x
where, x = 1 to x = 5
We know, the formula of rate of change is
Rate of change = ( f(b) - f(a) ) / (b - a)
for x = 5, for that put value of x in given function
f(x) = 5(2) ^ x
f(5) = 5(2) ^ 5
f(5) = 160
for x = 1, for that put value of x in given function
f(x) = 5(2) ^ x
f(1) = 5(2) ^ 1
f(1) = 10
Now, plug in the values in rate of change formula
Rate of change = ( f(5) - f(1) ) / (5 - 1)
= ( 160 - 10) / 4
= 150 / 4
= 37.5
Hence, the average rate of change is 37.5
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