Consider the standard form of an exponential function: y = a (b)^x
1. How does changing the base number (inside the parentheses) change your graph? (10 points)

2. How does changing the number outside the parentheses change your graph? (10 points)

Problem 1

If 0 < b < 1, then we have exponential decay. The curve will decrease downhill as you move from left to right.

If b > 1, then we have exponential growth and the curve goes uphill as we move from left to right.

Examples: y = 2(0.5)^x is exponential decay while y = 2(1.2)^x represents exponential growth.

Note that the base b cannot be negative.

Problem 2

Plug x = 0 into the general template given

y = a(b)^x

y = a(b)^0

y = a(1)

y = a

Plugging x = 0 leads to the output y = a

Therefore, the point (0,a) is on the curve. This is the y intercept. It's where the curve crosses the y axis. If you change the value of 'a', then you change the y intercept.

Examples:

based on context clues you gave i'm assuming the answer would be c.

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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