Question

The Quantity of an element is decaying over time such that the amount of material at

time is given by the funetion K (t) = 2000(0.9)^t+2. Write an equivalent
function of the form K (t) = ab^t

Answer 1

Below

Explanation:

= 2000 (.9)^2 (.9)^t

= 2000(.81)(.9)^t

= 1620 (.9)^t

Answer 2

`K(t)=1620(0.9)^(t)`

Explanation:

Given function:

`K(t)=2000(0.9)^(t+2)`

`\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:`

`\implies K(t)=2000(0.9)^(t)\cdot(0.9)^2`

Simplify:

`\implies K(t)=2000(0.9)^(t)\cdot0.81`

`\implies K(t)=0.81 \cdot 2000(0.9)^(t)`

`\implies K(t)=1620(0.9)^(t)`