Help me with this question (question in description)

Question

https://imgur.com/a/nVfiHBT

Answer 1

Nadine has a term deposit of $5250 at 4.8% per year. She receives the interest from the deposit each month

a. Write a sequence to show the accumulated interest Nadine will receive in the 1st 5 months

b. Draw a graph to show the terms of the sequence

c. What type of growth does the graph display? Explain

This is a beginner question to interest exponential growth. If Nadine deposits $5,250 in her bank account, each year the bank will add an additional 4.8% of $5,250 into her bank account, so how much will be in there after just one month.

The formula to calculate this is A (amount in bank after time, t) = P (principle) X (1 + rt)

r = interest rate per year in decimal form

t = amount of time in years

1st convert 4.8% to a decimal --> 4.8 / 100 = 0.048

Then convert 1 month to years = 1 month / 12 month/year = 1/12 = 0.08333 years

After one month there will be A = $5,250 (1 + 0.048 *0.0833) = $5,271

After 2 months or 2/12 = 0.1667 years

A = $5,250 (1 + 0.048 *0.1667) = $5,292

After 3 months or 3/12 = 0.25 years

A = $5,250 (1 + 0.048 *0.25) = $5,313

4 months - 4/12 = 0.333 years

A = $5,334

5 months - 0.4167 years

A = $5,355

b. The graph will have t as the x-axis and A as the y-axis and plot the following points

(1, 5271), (2, 5292), (3, 5313), (4, 5334), (5, 5355)

c. The graph shows exponential growth.

At first the growth is slow, then the growth is moderate but starts to increase. Over time the graph rapidly increases.