Exponential Function Solution Equation - Decay (Discrete, Mis-matched Time Units) - Scenario to Time (Level 1)

Exponential Function Solution Equation - Decay (Discrete, Mis-matched...

A toxin starts at a concentration of 800mg/L. Each daily dialysis reduces it by 3%. After a certain number of hours it has decreased to a concentration of 42mg/L.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 1 over 24 times \ln{\frac{42 over 800 }}{\ln{(1+0.03)}}$

b $A LaTex expression showing t = 24 times \ln{\frac{42 over 800 }}{\ln{(1-0.03)}}$

c $A LaTex expression showing t = 24 times \frac{\ln{42 times 800}}{\ln{(1-0.03)}}$

A charitable endowment starts with $900. Each daily it disburses 5% of its remaining funds. After a certain number of years its funds have decreased to $771.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 1 over 365 times \ln{\frac{771 over 900 }}{\ln{(1-0.05)}}$

b $A LaTex expression showing t = 1 over 365 times \frac{\ln{771 times 900}}{\ln{(1-0.05)}}$

c $A LaTex expression showing t = 365 times \ln{\frac{771 over 900 }}{\ln{(1+0.05)}}$

d $A LaTex expression showing t = 365 times \ln{\frac{771 over 900 }}{\ln{(1-0.05)}}$

A charitable endowment starts with $900. Each daily it disburses 2% of its remaining funds. After a certain number of years its funds have decreased to $830.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 365 times \ln{\frac{830 over 900 }}{\ln{(1+0.02)}}$

b $A LaTex expression showing t = 1 over 365 times \ln{\frac{830 over 900 }}{\ln{(1-0.02)}}$

c $A LaTex expression showing t = 365 times \ln{\frac{830 over 900 }}{\ln{(1-0.02)}}$

A charitable endowment starts with $600. Each yearly it disburses 8% of its remaining funds. After a certain number of months its funds have decreased to $10.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 12 times \frac{\ln{10 times 600}}{\ln{(1-0.08)}}$

b $A LaTex expression showing t = 12 times \ln{\frac{10 over 600 }}{\ln{(1-0.08)}}$

c $A LaTex expression showing t = 1 over 12 times \ln{\frac{10 over 600 }}{\ln{(1+0.08)}}$

A charitable endowment starts with $500. Each weekly it disburses 9% of its remaining funds. After a certain number of days its funds have decreased to $2.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 1 over 7 times \ln{\frac{2 over 500 }}{\ln{(1-0.09)}}$

b $A LaTex expression showing t = 7 times \ln{\frac{2 over 500 }}{\ln{(1-0.09)}}$

c $A LaTex expression showing t = 7 times \frac{\ln{2 times 500}}{\ln{(1-0.09)}}$

A charitable endowment starts with $200. Each yearly it disburses 9% of its remaining funds. After a certain number of months its funds have decreased to $0.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 12 times \ln{\frac{0 over 200 }}{\ln{(1-0.09)}}$

b $A LaTex expression showing t = 1 over 12 times \ln{\frac{0 over 200 }}{\ln{(1+0.09)}}$

c $A LaTex expression showing t = 12 times \frac{\ln{0 times 200}}{\ln{(1-0.09)}}$

d $A LaTex expression showing t = 1 over 12 times \ln{\frac{0 over 200 }}{\ln{(1-0.09)}}$

A charitable endowment starts with $900. Each yearly it disburses 4% of its remaining funds. After a certain number of months its funds have decreased to $17.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 1 over 12 times \ln{\frac{17 over 900 }}{\ln{(1-0.04)}}$

b $A LaTex expression showing t = 12 times \ln{\frac{17 over 900 }}{\ln{(1-0.04)}}$

A toxin starts at a concentration of 200mg/L. Each daily dialysis reduces it by 7%. After a certain number of weeks it has decreased to a concentration of 149mg/L.

Rearrange the exponential equation to solve for for the time given this scenario?

a $A LaTex expression showing t = 7 times \ln{\frac{149 over 200 }}{\ln{(1+0.07)}}$

b $A LaTex expression showing t = 1 over 7 times \frac{\ln{149 times 200}}{\ln{(1-0.07)}}$

c $A LaTex expression showing t = 1 over 7 times \ln{\frac{149 over 200 }}{\ln{(1-0.07)}}$

Exponential Function Solution Equation - Decay (Discrete, Mis-matched Time Units) - Scenario to Time

Exponential Function Solution Equation - Decay (Discrete, Mis-matched Time Units) - Scenario to Time Worksheet