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Camryn puts $400 into a savings account that earns 6% annually. the amount in her account can
be modeled by c(t) = 400(1.06)", where t is the time in years. which expression best
approximates the amount of money in her account using a weekly growth rate?
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1 Answer

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The exponential function that approximates the amount of money in her account using a weekly growth rate is:

[tex]c_w(t) = 400(1.001154)^{\frac{t}{52}}[/tex]

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

- A(0) is the initial value.

- r is the growth rate, as a decimal

In this problem, the yearly function is:

[tex]c(t) = 400(1.06)^t[/tex]

Considering that a year has 52 weeks, we have that:

0.06/52 = 0.001154

Hence:

[tex]c_w(t) = 400(1.001154)^{\frac{t}{52}}[/tex]

More can be learned about exponential functions at  

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