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3 years ago

In general, the y intercept of the function F(x)= a•b^x is the point

Mathematics

1 answer:

serg [7]3 years ago

4 0

The y intercept of this function is always (0, a).

This is because when we place 0 in for x (which is the only way it'll be on the y-axis, we get 'a' as a result. This is because of the rule that raising anything to the 0th power will result in the number 1 and multiplying anything by 1 gives us the same number. See the work below for the example.

F(x) = a*b^x

F(0) = a*b^0

F(0) = a*1

F(0) = a

And for an example with a random number, we'll use a = 5 and b = 3

F(x) = 5*3^x

F(0) = 5*3^0

F(0) = 5*1

F(0) = 5

No matter what a and b equal, the intercept will be the a value.

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Hunter-Best [27]

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence ( $a_{i}$ ) (range) and their respective indexes ( $i$ ) (domain):

$i$ $a_{i}$

1 6

2 11

3 16

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b) The algebraic expression for the general term of the sequence is $a(i) = 6 + 5\cdot (i - 1)$ .

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Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence ( $a_{i}$ ) (range) and their respective indexes ( $i$ ) (domain):

$i$ $a_{i}$

1 6

2 11

3 16

4 21

5 26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

$a(i) = a_{1} + r\cdot (i - 1)$ (1)