t(n)=2n + 8
Find the explicit equation for the sequence: 10, 12, 14, 16, …
The function t(n) you have provided is a linear function with a slope of 2 and a y-intercept of 8. This means that the value of t(n) increases by 2 every time n is increased by 1.
To better understand this, let’s take a few examples:
When n=0, t(n) = 8
When n=1, t(n) = 10
When n=2, t(n) = 12
When n=3, t(n) = 14
We can see that as we increase the value of n, the function t(n) increases as well, with a constant slope of 2.
It’s important to note that a linear function always has a constant rate of change, which in this case is 2. We can use this information to find answers to various questions related to the function.
For example, we can find the value of n when t(n)=20 as follows:
2n + 8 = 20
2n = 12
n = 6
Therefore, when n=6, the value of t(n) is 20.
Similarly, we can find the value of t(n) when n=4 as follows:
t(4) = 2*4 + 8
t(4) = 16
Therefore, when n=4, the value of t(n) is 16.
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