# What is the growth factor, initial amount for M(t)=8(2)^(1/6t)?

Jun 22, 2018

Growth factor = 2
Initial Amount = 8

#### Explanation:

You're using the form $A \left(t\right) = {A}_{0} {\left(b\right)}^{\frac{t}{k}}$, where:
${A}_{0}$ = the initial amount
$b$ = the growth factor
$t$ = the amount of time elapsed
$k$ = 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 $t$ in the fraction in the exponent:

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