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.

The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time the graph of the exponential function relate to time and money.

Given that,

Leticia invests $200 at 5% interest.

If y represents the amount of money after x time periods.

We have to determine,

Which describes the graph of the exponential function relating time and money?

According to the question,

The graph represents the exponential function relating time and money.

Where y represents the amount of money after x time periods.

After 1 period the amount of money is,

[tex]\rm f(x) = 200 + 200\left(\dfrac{5}{100}\right)\\\\f(x) = 200(1+0.5)\\\\f(x)= 200(1.5)\\\\[/tex]

After 2 periods the amount is,

[tex]\rm f(x) = 200(1.5) \times (1.5)\\\\f(x) = 200. (1.5)^2[/tex]

After 3 periods the amount is,

[tex]\rm f(x) = 200(1.5)^2 \times (1.5)\\\\f(x) = 200. (1.5)^3[/tex]

Therefore,

The amount after x period is,

[tex]\rm f(x) = 200(1.5)^x[/tex]

The initial value is when x = 0,

[tex]\rm y = 200 (1.05)^0 \\\\y = 200\times 1\\\\y = 200[/tex]

And the increasing factor is 1.05 because any value is the previous one times 1.05.

Hence, The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time the graph of the exponential function relate to time and money.

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https://brainly.com/question/17407467