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.

I know that just the answer is not enough. You need to understand why and how. So I will explaing the steps.

First you need to state the equation that represents the function.

Investment is $200 and interest rate is 5%, y is the amount of money after x periods.

Note that after 1 period the amount of money is 200 plus 5% interest, which is 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After 2 periods the amount is 200(1.05)*(1.05) = 200 (1.05)^2

After 3 periods the amount is 200 (1.05)^3

And now you can deduce that after x periods y = 200 (1.05)^x

You can then analyze the function to predict the shape and critical points of the graph.

The answers are based in the initial value and the increasing factor.

The initial value is when x = 0, which yields to y = 200 (1.05)^0 = 200*1 = 200

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

Then the answer is the first option. The initial value is 200 and the graph increases by a factor of 1.05 per 1 unit increase in time. 

The exponential form of the equation produced using the information given is the initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time.

General form of an exponential growth relation :

y = final amount ; A = initial value ; r = growth rate

Hence, we'll have :

Therefore, comparing the equation to the general format of am exponential growth relation, the option A is the correct answer.

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