Question

Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function.

Answer 1

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 $f(t)=P(1+r)^{t}$ , 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 $5000(1.07)^{t}=B$

∵ The function is $5000(1.07)^{t}=B$

∵ 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

∵ $(1+r)^{t}=(1.07)^{t}$

∴ 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

∴ $5000(1.07)^{5}=B$

∴ B = 7012.76

c) Sue will have $7012.76 after 5 years

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