Question

determining the appearance of a graph

leticia invests $200 at 5% interest. if \\(y\\) represents the amount of money after \\(x\\) time periods, which describes the graph of the exponential function relating time and money?

• the initial value of the graph is 200. the graph increases by a factor of 1.05 per 1 unit increase in time.
• the initial value of the graph is 200. the graph increases by a factor of 5 per 1 unit increase in time.
• the initial value of the graph is 500. the graph increases by a factor of 2 per 1 unit increase in time.
• the initial value of the graph is 500. the graph increases by a factor of 1.02 per 1 unit increase in time.

Explanation:

Determine the initial value

$$ y(0) = 200 $$

Determine the growth factor

$$ b = 1 + r = 1 + 0.05 = 1.05 $$

Formulate the exponential function

$$ y = 200(1.05)^x $$

Answer:

• (A) The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time. (Correct answer)
• (B) The initial value of the graph is 200. The graph increases by a factor of 5 per 1 unit increase in time.
• (C) The initial value of the graph is 500. The graph increases by a factor of 2 per 1 unit increase in time.
• (D) The initial value of the graph is 500. The graph increases by a factor of 1.02 per 1 unit increase in time.