Evaluate. 4^3⋅(100÷25)−5^0 Enter your answer in the box.
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Answer:
<em>The function is of an exponential growth type</em>
<em>Rate of change is 240%</em>
Step-by-step explanation:
<u>Exponential Function</u>
The expression of an exponential function is
For a,b,c constants.
1.
The function will be of an exponential growth type if, when x increases, f increases. That behavior comes from the combination of the three constants a,b,c. The best approach to find that out is by taking the first derivative
Since is always positive, the product of b.c.lna must be positive to make f increasing. For example, if a>1 and both b and c are of the same sign, f increases for all x. If 0<a<1, then, since lna<0, the product b.c must be negative, i.e. both should have different signs
The function is expressed as
we can see a>1, b and c are positive, so the function is of an exponential growth type.
2.
Talking about rates change of real functions takes us to the derivative function. We have already seen the derivative is dependent on all three constants and also of the value of x, so it cannot be predicted as a fixed percentage.
Now, if we picture the function as the general term of a sequence, where x can only take natural values, we can say
Each term is obtained as the previous term by 2.4. It's accurate to say the rate of change is 240%