Question

3. A geometric sequence g starts at 500 and has a growth factor of 0.6. Sketch a graph of g

showing the first 5 terms.

Answer 1

To sketch the graph of a geometric sequence starting at 500 with a growth factor of 0.6, we can use the formula: t_n = a * r^(n-1). The graph will show a downward trend as the term number increases, indicating exponential decay.

Step-by-step explanation:

To sketch the graph of a geometric sequence starting at 500 with a growth factor of 0.6, we can use the formula:

tn = a * r^(n-1)

where tn is the nth term, a is the first term, r is the growth factor, and n is the term number.

For the first 5 terms, we have:

• t1 = 500
• t2 = 500 * 0.6^1 = 300
• t3 = 500 * 0.6^2 = 180
• t4 = 500 * 0.6^3 = 108
• t5 = 500 * 0.6^4 = 65

Now, we can plot these points on a graph, with the term number (x-axis) and the term value (y-axis).

The graph will show a downward trend as the term number increases, indicating exponential decay.

Answer 2

Here you go! Sorry if its not in the correct format.

Hope this helps!