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Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. A new savings account is opened with $200 and gains 3.1% yearly for 8 years. The exponential function that models the situation is . After 8 years, the savings account has $ . , , , and .

Sagot :

MrRoyalidn

Answer:

[tex](a)\ f(8) = 200(1 + 3.1\%)^8[/tex]

(b) After 8 years, the savings account has $255.32

Step-by-step explanation:

Given

[tex]a = 200[/tex] ---- initial (i.e. when t = 0)

[tex]r =3.1\%[/tex]

[tex]t = 8[/tex]

Solving (a): Model the situation

For growth, an exponential function is represented as:

[tex]f(t) = a(1 + r)^t[/tex]

This gives:

[tex]f(8) = 200(1 + 3.1\%)^8[/tex]

Solving (b): The solution to (a)

We have:

[tex]f(8) = 200(1 + 3.1\%)^8[/tex]

Express percentage as decimal

[tex]f(8) = 200(1 + 0.031)^8[/tex]

[tex]f(8) = 200(1.031)^8[/tex]

[tex]f(8) = 200*1.2766[/tex]

[tex]f(8) = 255.32[/tex]

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