What is the growth factor, initial amount for $M (t) = 8 {(2)}^{\frac{1}{6} t}$ $M(t)=8(2)^(1/6t)$ ?

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What is the growth factor, initial amount for $M (t) = 8 {(2)}^{\frac{1}{6} t}$ $M(t)=8(2)^(1/6t)$ ?

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Answer 1 · 2018-06-22T14:57:48

Growth factor = 2
Initial Amount = 8

Explanation:

You're using the form $A (t) = A_{0} {(b)}^{\frac{t}{k}}$ $A(t)=A_0(b)^(t/k)$ , where:
$A_{0}$ $A_0$ = the initial amount
$b$ $b$ = the growth factor
$t$ $t$ = the amount of time elapsed
$k$ $k$ = the amount of time it takes to double/triple/etc.

Note: M(t) and A(t) are the same, just using different variables.

Your equation represents a doubling in whatever the problem applies to. It takes 6 years to double. In order to avoid confusion, you can place the $t$ $t$ in the fraction in the exponent:

$M (t) = 8 {(2)}^{\frac{t}{6}}$ $M(t)=8(2)^(t/6)$

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What is the growth factor, initial amount for $M (t) = 8 {(2)}^{\frac{1}{6} t}$ $M(t)=8(2)^(1/6t)$ ?

1 Answer

Explanation:

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What is the growth factor, initial amount for $M (t) = 8 {(2)}^{\frac{1}{6} t}$ $M(t)=8(2)^(1/6t)$ ?