a) 5000 represents the initial amount that Sue invested in a money market account
b) The annual percentage rate is 7%
c) Sue will have $7012.76 after 5 years
Step-by-step explanation:
The exponential growth function is [tex]f(t)=P(1+r)^{t}[/tex] , where
- r is the rate of growth in decimal
- P is the initial amount
- t is the time
Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function [tex]5000(1.07)^{t}=B[/tex]
∵ The function is [tex]5000(1.07)^{t}=B[/tex]
∵ The form of the exponential growth function is tex]f(t)=P(1+r)^{t}[/tex]
- By comparing the two functions
∴ P = 5000
∵ P is the initial amount
∴ The initial amount is 5000
a) 5000 represents the initial amount that Sue invested in a money market account
∵ [tex](1+r)^{t}=(1.07)^{t}[/tex]
∴ 1 + r = 1.07
- Subtract 1 from both sides
∴ r = 0.07
∵ r is the annual rate in decimal
∵ 0.07 × 100% = 7%
∴ The annual rate is 7%
b) The annual percentage rate is 7%
∵ t = 5
- Substitute the value of t in the function
∴ [tex]5000(1.07)^{5}=B[/tex]
∴ B = 7012.76
c) Sue will have $7012.76 after 5 years
Learn more:
You can learn more about annual rate in brainly.com/question/3614284
#LearnwithBrainly
