Need with this problem. it's taken from the chapter "logarithm and polynomials".

see explanation

Step-by-step explanation:

Given

A = 80 ← initial amount is 80

The amount is halved in 1.5 days, hence

(a)

80 = 40 ( divide both sides by 80 )

= 0.5

Take the natural log of both sides

ln = ln 0.5, thus

-1.5k ln e = ln 0.5 ← ln e = 1

- 1.5k = ln 0.5 ( divide both sides by - 1.5 )

k = = 0.462 ( 3 dec. places )

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(b)

80 = 5 ( divide both sides by 80 )

= 0.0625

Take the natural log of both sides

ln = ln 0.0625

- 0.462t = ln 0.0625 ( divide both sides by - 0.462

t = ≈ 6 days

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(c)

80 = 80 × ≈ 1.25 g

three-fourths of an hour

36÷48=0.75

0.75=