A chemical substance has a decay rate of 6.1% per day. The rate of change of an

ID: 2887196 • Letter: A

Question

A chemical substance has a decay rate of 6.1% per day. The rate of change of an amount N of the chemical is given by the equation dN/dt=-0.061N

where t is the number of days since decay began. Complete parts ?a) through c)

a) Let N0 represent the amount of the chemical substance at

t=0. Find the exponential function that models the situation.

?b) Suppose that 300 g of the chemical substance is present at t=0.

How much will remain after 3 ?days?

After 3 ?days, ___ g will remain.

?(Round to the nearest whole number as? needed.)

?c) After how many days will half of the 300g of the chemical substance? remain?

After ___ days, half of the chemical substance will remain.

?(Round to one decimal place as? needed.)

dN/dt = -0.061N

dN / N = -0.061 dt

Integrating both sides

ln N = -0.061t + N0

N = N0e-0.061t

b. N = 300 e -0.061(3)

N = 250gm

c. Half of 300= 150

150 = 300 e-0.061t

ln (1/2)= -0.061t

t= 11.4 days

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