For the following set of ordered pairs, determine if the mapping is linear or exponential: - (1, 2), (2, 4), (3, 8), (4, 16) Justify your answer. Given a linear mapping with the rule y = 3x + 2, calculate the output values for x = 0, 1, 2, and 3. Organize your results in a table. A mobile phone plan charges a fixed fee of GH₵10 plus GH₵0.50 per minute. Write the rule for this mapping in the form y = mx + c, where x represents minutes and y represents total cost. Identify the constant difference in the domain and co-domain for the following mapping, then determine the rule: - Domain: 2, 4, 6, 8 - Co-domain: 7, 13, 19, 25 For the mapping y = 2x + 1, create a table of values for x = -2, -1, 0, 1, 2 and explain what the values of m and c represent. Given the rule y = -2x + 5, determine the output when x = 3 and explain what this ordered pair represents in the context of the mapping. A taxi charges GH₵2.50 per kilometre plus a fixed charge of GH₵5. Write the mapping rule and calculate the cost for a 15 km journey.

The y-values are 2, 4, 8, 16.
Differences:
$4 - 2 = 2$
$8 - 4 = 4$
$16 - 8 = 8$
Since the differences are not constant (2, 4, 8), the mapping is not linear.

Ratios:
$\frac{4}{2} = 2$
$\frac{8}{4} = 2$
$\frac{16}{8} = 2$
Since there is a constant ratio of 2 between consecutive y-values, the mapping is exponential.

The mapping is exponential because there is a constant ratio of 2 between consecutive y-values.
$\boxed{\text{Exponential}}$

15. Given a linear mapping with the rule y = 3x + 2, calculate the output values for x = 0, 1, 2, and 3. Organize your results in a table.

$y = 3(0) + 2 = 0 + 2 = 2$

$y = 3(1) + 2 = 3 + 2 = 5$

$y = 3(2) + 2 = 6 + 2 = 8$

$y = 3(3) + 2 = 9 + 2 = 11$

$\boxed{\text{Table above}}$

16. A mobile phone plan charges a fixed fee of GH₵10 plus GH₵0.50 per minute. Write the rule for this mapping in the form y = mx + c, where x represents minutes and y represents total cost.

The fixed fee is GH₵10, so $c = 10$.

The charge per minute is GH₵0.50, so $m = 0.50$.

Substituting the values of m and c:
$y = 0.50x + 10$

The rule is $\boxed{y = 0.50x + 10}$.

17. Identify the constant difference in the domain and co-domain for the following mapping, then determine the rule: - Domain: 2, 4, 6, 8 - Co-domain: 7, 13, 19, 25

Differences:
$4 - 2 = 2$
$6 - 4 = 2$
$8 - 6 = 2$
The constant difference in the domain is 2.

Differences:
$13 - 7 = 6$
$19 - 13 = 6$
$25 - 19 = 6$
The constant difference in the co-domain is 6.

The slope $m = \frac{\text{change in y}}{\text{change in x}} = \frac{6}{2} = 3$.

Using the point $(2, 7)$ and $m = 3$ in $y = mx + c$:
$7 = 3(2) + c$
$7 = 6 + c$
$c = 7 - 6$
$c = 1$

The rule is $y = 3x + 1$.

The constant difference in the domain is 2.
The constant difference in the co-domain is 6.
The rule is $\boxed{y = 3x + 1}$.

18. For the mapping y = 2x + 1, create a table of values for x = -2, -1, 0, 1, 2 and explain what the values of m and c represent.

$y = 2(-2) + 1 = -4 + 1 = -3$

$y = 2(-1) + 1 = -2 + 1 = -1$

$y = 2(0) + 1 = 0 + 1 = 1$

$y = 2(1) + 1 = 2 + 1 = 3$

$y = 2(2) + 1 = 4 + 1 = 5$

In the equation $y = 2x + 1$:

• $m = 2$ represents the slope of the line, indicating that for every unit increase in x, y increases by 2 units.
• $c = 1$ represents the y-intercept, which is the value of y when x is 0.

$\boxed{\text{Table above, m is slope, c is y-intercept}}$

19. Given the rule y = -2x + 5, determine the output when x = 3 and explain what this ordered pair represents in the context of the mapping.

Substitute $x = 3$ into the rule:
$y = -2(3) + 5$
$y = -6 + 5$
$y = -1$

The output when $x = 3$ is $y = -1$. This forms the ordered pair $(3, -1)$.
This ordered pair represents a specific point on the line defined by the mapping rule $y = -2x + 5$. It means that when the input is 3, the corresponding output is -1.

The output when $x = 3$ is $\boxed{-1}$.
The ordered pair $(3, -1)$ represents a point on the line where an input of 3 yields an output of -1.

20. A taxi charges GH₵2.50 per kilometre plus a fixed charge of GH₵5. Write the mapping rule and calculate the cost for a 15 km journey.

Let y be the total cost and x be the number of kilometres.
The charge per kilometre is GH₵2.50, so $m = 2.50$.
The fixed charge is GH₵5, so $c = 5$.
The mapping rule is $y = 2.50x + 5$.

Substitute $x = 15$ into the rule:
$y = 2.50(15) + 5$
$y = 37.50 + 5$
$y = 42.50$

The mapping rule is $\boxed{y = 2.50x + 5}$.
The cost for a 15 km journey is $\boxed{\text{GH₵}42.50}$.