Question

use properties of exponents to write the function in the form f(t)=ka^t, where k is a constant.2^2t+3

Answer 1

`8*4^t`Step-by-step explanation:

f(t) = ka^t

`2^(2t+3)​is\text{ the same as }2^{\mleft\{2t\mright\}}*2^3`

Reason: Product of exponents

a^m + a^p = a^(m+p)

when the base is the same and the sign between both base is multiplication, the exponents are added together after picking one of the base

`\begin{gathered} 2^(2t+3)​=2^{\{2t\}}*2^3 \\ =2^(2t)*8 \end{gathered}`
`\begin{gathered} 2^{\{2t\}}=2^(2* t) \\ =4^t \\ 2^(2t)*8\text{ }=4^t*8 \end{gathered}`
`\begin{gathered} In\text{ the form:}f\mleft(t\mright)=ka^t \\ 2^(2t+3)​=8*4^t \\ k\text{ = constant= 8} \end{gathered}`