Question

2.02 Graded Assignment: Graphing Exponential Equations

Answer 1

An exponential function is a function that has the form y = ab^x, where a represents the initial value, and b represents the rate

(1) How to fill the table

The exponential function is given as:

$y = 0.50(1.06)^x$

When x = 0, we have:

$y = 0.50 * (1.06)^0 = 0.50$

When x = 10, we have:

$y = 0.50 * (1.06)^{10} = 0.90$

When x = 20, 30 and 40 we have:

$y = 0.50 * (1.06)^{20} = 1.60$

$y = 0.50 * (1.06)^{30} = 2.87$

$y = 0.50 * (1.06)^{40} = 5.14$

So, the complete table is:

Years after 1950 X : 0 | 10 | 20 | 30 | 40

Ticket Price $ Y     : 0.50 | 0.90 | 1.60 | 2.87 | 5.14

(2) The y-intercept and the rate

The prices look reasonable.

The y-intercept is when x = 0.

So, the value of the y-intercept is 0.50

Also, the rate represents a growth.

This is so, because the rate is greater than 1

(3) The graph

See attachment for the graph of the exponential function

(4) The prices in 2000 and 2010

When x = 50 and 60, we have:

$y = 0.50 * (1.06)^{50} = 9.21$

$y = 0.50 * (1.06)^60} = 16.49$

Hence, the prices in 2000 and 2010 are $9.21 and $16.49

Read more about exponential functions at:

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