Question

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)

Answer 1

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.

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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:

• y = 2(5)^x has y intercept 2
• y = 3(0.8)^x has y intercept 3