Respuesta :
Problem 1, part (a)
t = number of years
A = value of the necklace after t years
3.2% = 3.2/100 = 0.032
If the necklace starts off being $1, then after t years, it will have this value
A = 1*(1 + 0.032)^t
A = 1.032^t
You were close, but forgot about the exponent t
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Problem 1, part (b)
Since t represents the number of years, this means 12t represents the number of months, because there are 12 months in a year.
The annual growth rate is 3.2%, which converts to 0.032
Divide this over 12 and we get the approximate value 0.032/12 = 0.00267
So we get this new equivalent function
A = 1*(1+0.00267)^(12t)
A = 1.00267^(12t)
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Problem 2, part (a)
t = number of years
12t = number of months
The ring's value goes at a rate of 0.33% per month, which converts to the decimal form 0.0033
The value of the ring is
B = 1*(1 + 0.0033)^(12t)
B = 1.0033^(12t)
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Problem 2, part (b)
We'll take the reverse approach in what we did with part (b) of the previous problem. There we divided by 12 to go from an annual rate to a monthly rate.
We'll multiply by 12 to go from the monthly growth rate to the annual growth rate.
The monthly growth rate of 0.33% turns into the annual growth rate of 12*0.33% = 3.96%, and that turns into the decimal form 0.0396
So,
B = 1*(1+0.0396)^t
B = 1.0396^t
represents the value of the ring after t years.
