Problem

$B(t)~=~2500(1.005)^{52t}$, where $t$ is in years, $B$ is in dollars, and $1.005$ is the weekly growth factor. Rewrite the model to display the annual factor, then state the initial balance, annual factor, and annual growth rate.

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B(t)=2500[(1.005)/52]t. The annual factor is about 0.01933, so the annual decay rate is about 98.067%, applied to a $2,500 initial balance.

B(t)=2500[(1.005)⁵²]t. The annual factor is about 1.29609, so the annual growth rate is about 129.609%, applied to a $2,500 initial balance.

B(t)=2500[(1.005)⁵²]t. The annual factor is about 1.29609, so the annual growth rate is about 29.609%, applied to a $2,500 initial balance.

B(t)=2500(1.26)t. The annual factor is exactly 1.26, so the annual growth rate is exactly 26%, applied to a $2,500 initial balance.

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