Home
Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes
Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation
Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
Sign InJoin

Exponential Function Solving - Decay (Discrete) Equation to Rate

Level 1

This math topic focuses on solving for the rate in exponential decay functions. It includes problems involving real-life applications such as the decline of toxin concentration with hourly or weekly dialysis, yearly breeding cycles of whale and bird populations, and monthly or yearly disbursements of a charitable endowment fund's balance. Each question requires determining the exponential decay rate from given data points and understanding how the initial and remaining values decline over specific time intervals.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
WorksheetView

Exponential Function Solving - Decay (Discrete) Equation to Rate Worksheet

Mobius Math Academy logo
Exponential Function Solving - Decay (Discrete) Equation to Rate
1
Solve for the rate given this model of a decline of a toxin concentration (hourly dialysis)?
A LaTex expression showing 323 =500 times (1-r) to the power of (6)
a A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 9 + r = -(C over C sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 6 + r = -(C over C sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing 7 + r = -(C over C sub 0 ) to the power of 1 over t + 1
2
Solve for the rate given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing 331 =400 times (1-r) to the power of (2)
a A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 5 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing 4 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 9 + r = -(P over P sub 0 ) to the power of 1 over t + 1
3
Solve for the rate given this model of a balance of a charitable endowment (monthly disbursements)?
A LaTex expression showing 518 =800 times (1-r) to the power of (7)
a A LaTex expression showing 0 + r = -(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 5 + r = -(P over P sub 0 ) to the power of 1 over t + 1
4
Solve for the rate given this model of a decline of a toxin concentration (weekly dialysis)?
A LaTex expression showing 376 =500 times (1-r) to the power of (3)
a A LaTex expression showing 1 + r = -(C over C sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 2 + r = -(C over C sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 6 + r = -(C over C sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t - 1
5
Solve for the rate given this model of a decline of a bird population (yearly breeding cycle)?
A LaTex expression showing 293 =400 times (1-r) to the power of (5)
a A LaTex expression showing 7 + r = -(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 1 + r = -(P over P sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing 3 + r = -(P over P sub 0 ) to the power of 1 over t + 1
6
Solve for the rate given this model of a decline of a toxin concentration (weekly dialysis)?
A LaTex expression showing 255 =300 times (1-r) to the power of (8)
a A LaTex expression showing 3 + r = -(C over C sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 2 + r = -(C over C sub 0 ) to the power of 1 over t + 1
7
Solve for the rate given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 424 =700 times (1-r) to the power of (6)
a A LaTex expression showing 2 + r = -(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 8 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
d A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
8
Solve for the rate given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing 398 =600 times (1-r) to the power of (8)
a A LaTex expression showing 8 + r = -(P over P sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing 2 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1