Option C
The function for P representing the amount of money Philip will have after T years p = 1200(1.09)t
Solution:
Given, Philip deposited $1,200 in a bank that is paying 9% interest rate once a year.
We have to select a function for P representing the amount of money he’ll have after T years .
Now, let us calculate amount after 1 year, then t = 1, rate = 9% = [tex]\frac{9}{100}[/tex] =0.09, amount = $1200.
Amount in bank after 1 year = amount deposited + interest gained
⇒1200 + 1200 x 0.09 x 1 ⇒ 1200(1 + 0.09)
⇒Hence our answer is 1200(1.09)
Now, put t = 1 in given options.
P= 1.09t ⇒ p = 1.09 ⇒ doesn’t match with our answer.
P= 1,200(1.0075)t ⇒ p = 1200(1.0075) ⇒ doesn’t match with our answer.
P=1,200(1.09)t ⇒ p = 1200(1.09) ⇒ matches with our answer.
P=1,200(0.09)t ⇒ p = 1200(0.09) ⇒ doesn’t match with our answer.
P=1,200e^0.09t ⇒ p = 1200e^0.09 ⇒ doesn’t match with our answer.
Hence, the correct representation is p = 1200(1.09)t. Thus option C is correct
