Question

Muke is sick with the flu but he still cors to school on monday. He areives at 8am and by 9am (hour 1) muke has already infectedtwo of his friends

Answer 1

`\begin{array}{ccccccccc}{Hours} & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} \ \\ {Persons} & {1} & {2} & {4} & {8} & {16}& {32} & {64} & {128} \ \end{array}`

Explanation:

Given

See attachment for complete question

Solving (a): Complete the table

Let

`x = hours`

`y = persons`

From the table question, we have:

`(x_1,y_1) = (0,1)`

`(x_2,y_2) = (1,2)`

`(x_3,y_3) = (2,4)`

The pattern follows that, an increment in x by doubles the value of 1.

So, the other values are:

`(x_4,y_4) = (3,8)`

`(x_5,y_5) = (4,16)`

`(x_6,y_6) = (5,32)`

`(x_7,y_7) = (6,64)`

`(x_8,y_8) = (7,128)`

So, the complete table is:

`\begin{array}{ccccccccc}{Hours} & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} \ \\ {Persons} & {1} & {2} & {4} & {8} & {16}& {32} & {64} & {128} \ \end{array}`

Solving (b): The graph

The table follows an exponential function:

`y = ab^x`

We have:
`(x_1,y_1) = (0,1)`

This gives:

`y = ab^x`

`1 = ab^0`

`b^0 \to 1`

So:

`1 = a*1`

`1 = a`

`a =1`

Also:
`(x_5,y_5) = (4,16)`

This gives:

`y = ab^x`

`16 = 1 * b^4`

`16 = b^4`

`16 \to 2^4`

So:

`2^4 = b^4`

Cancel the exponents (4)

`2 =b`

`b = 2`

So, the function
`y = ab^x` is:

`y = 2^x`

See attachment 2 for graph