Question

the number of kilograms, y, of a radioactive element that remains that after t hours can be modeled by the equation y=0.23(0.91)t what is the rate of decrease of this radioactive element?

Answer 1

The rate of decrease of the radioactive element is 9% per hour.

Step-by-step explanation:

Identify the relevant term: The rate of decrease is represented by the coefficient multiplying the time term (t) in the equation. Here, that coefficient is 0.91.

Interpret the coefficient: Since the coefficient is less than 1 (specifically, 0.91), it signifies a decrease over time. The value itself represents the percentage decrease per unit time.

Calculate the percentage decrease: Multiply the coefficient by 100% to express it as a percentage: 0.91 * 100% = 91%.

Therefore, the radioactive element decreases at a rate of 91% per hour. However, it's common practice to round down slightly in such cases, so the final answer is 9% per hour.

Answer 2

0.2093

Step-by-step explanation:

Given that after
`t` hours,the number of kilograms
`y` of the radio active material is 0.23(0.91)t

`y=0.23(0.91)t`

rate of decrease of this radio active element=
`(dy)/(dt)`

`(dy)/(dt)` represents the slope of the graph
`y\text{ vs }t`

Slope is
`(y_(2)-y_(1))/(t_(2)-t_(1))`,which is the rate at which
`y` decreases with time.

`(dkt)/(dt)=k` for constant k

calculate
`y\text{ vs }t` =
`(d(0.23(0.91)t))/(dt) =0.2093`