Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left? a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)

(a)

(b) There will be 1lb left after 14 hours

Step-by-step explanation:

Solving (a): The equation

Since the substance decomposes at a proportional rate, then it follows the following equation

Where

Initial Amount

rate

time

Amount at time t

Solving (b):

We have:

First, we calculate k using:

This gives:

Substitute:

Divide both sides by 4

Take natural logarithm of both sides

This gives:

Solve for k

So, we have:

To calculate the time when 1 lb will remain, we have:

So, the equation becomes

Divide both sides by 8

Take natural logarithm of both sides

Solve for t

--- approximated

not sure but it may be b, as i said i'm not sure.