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How does g(t) = 4t change over the interval t = 3 to t = 4?

How does g(t) = 4t change over the interval t = 3 to t = 4?-example-1
User MarkNS
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2 Answers

16 votes
16 votes

The function
\text{g(t)} = 4^t over the interval is that g(t) increases by a factor of 4

Finding the change of the function over the interval

From the question, we have the following parameters that can be used in our computation:


\text{g(t)} = 4^t

The interval is given as

From t = 3 to t = 4

The function is an exponential function

This means that it does not have a constant average rate of change

So, we have


\text{g(3)} = 4^3 = 64


\text{g(4)} = 4^4 = 256

Next, we have

Change = 256/64

Evaluate

Change = 4

Hence, the change of the function over the interval is that g(t) increases by a factor of 4

User Rob Hyndman
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20 votes
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Over the interval t = 3 to t = 4, g(t) increases.

The increasing factor (f) is computed as follows:


f=(g(4))/(g(3))

where g(4) is g(x) at t = 4, and g(3) is g(x) at t = 3. Substituting with the formula of g(t) and evaluating each expression, we get:


\begin{gathered} f=(4^4)/(4^3) \\ f=(4\cdot4^3)/(4^3) \\ f=4 \end{gathered}

Then, g(t) increases by a factor of 4

User KawaLo
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