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 Starting Value

Level 1

This math topic focuses on solving exponential decay equations to find the starting values in various contexts. Key skills practiced include manipulating exponential functions to isolate and solve for the initial quantity, decoding mathematical models representing declines (such as populations and concentrations), and understanding discrete exponential decay through yearly or daily cycles. This is framed within real-world scenarios like the decrease in whale populations and the reduction of toxin concentrations, helping to bridge abstract math concepts with practical applications.

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

more
WorksheetView

Exponential Function Solving - Decay (Discrete) Equation to Starting Value Worksheet

Mobius Math Academy logo
Exponential Function Solving - Decay (Discrete) Equation to Starting ...
1
Solve for the starting population given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing 234 =P sub 0 times (1-0.06) to the power of (4)
a A LaTex expression showing 3 + P sub 0 = P times (1-r) to the power of t
b A LaTex expression showing P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 3 + P sub 0 = P over (1+r) to the power of t
d A LaTex expression showing 8 + P sub 0 = P times (1-r) to the power of t
2
Solve for the starting population given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing 156 =P sub 0 times (1-0.03) to the power of (8)
a A LaTex expression showing 3 + P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 1 + P sub 0 = P times (1-r) to the power of t
d A LaTex expression showing 9 + P sub 0 = P times (1-r) to the power of t
3
Solve for the starting cash given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 141 =P sub 0 times (1-0.09) to the power of (8)
a A LaTex expression showing 8 + P sub 0 = P times (1-r) to the power of t
b A LaTex expression showing 6 + P sub 0 = P over (1+r) to the power of t
c A LaTex expression showing P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing 4 + P sub 0 = P over (1+r) to the power of t
4
Solve for the starting cash given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 150 =P sub 0 times (1-0.04) to the power of (7)
a A LaTex expression showing P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 2 + P sub 0 = P times (1-r) to the power of t
c A LaTex expression showing 6 + P sub 0 = P over (1+r) to the power of t
d A LaTex expression showing 2 + P sub 0 = P over (1+r) to the power of t
5
Solve for the starting concentration given this model of a decline of a toxin concentration (daily dialysis)?
A LaTex expression showing 553 =C sub 0 times (1-0.02) to the power of (4)
a A LaTex expression showing C sub 0 = C over (1-r) to the power of t
b A LaTex expression showing 9 + C sub 0 = C times (1-r) to the power of t
c A LaTex expression showing 2 + C sub 0 = C over (1+r) to the power of t
d A LaTex expression showing 6 + C sub 0 = C times (1-r) to the power of t
6
Solve for the starting cash given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 707 =P sub 0 times (1-0.04) to the power of (3)
a A LaTex expression showing 7 + P sub 0 = P times (1-r) to the power of t
b A LaTex expression showing 1 + P sub 0 = P times (1-r) to the power of t
c A LaTex expression showing P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing 9 + P sub 0 = P times (1-r) to the power of t
7
Solve for the starting population given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing 121 =P sub 0 times (1-0.08) to the power of (6)
a A LaTex expression showing 7 + P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing P sub 0 = P over (1-r) to the power of t
c A LaTex expression showing 2 + P sub 0 = P times (1-r) to the power of t
8
Solve for the starting cash given this model of a balance of a charitable endowment (daily disbursements)?
A LaTex expression showing 293 =P sub 0 times (1-0.06) to the power of (5)
a A LaTex expression showing 9 + P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing 3 + P sub 0 = P times (1-r) to the power of t
c A LaTex expression showing P sub 0 = P over (1-r) to the power of t
d A LaTex expression showing 8 + P sub 0 = P over (1+r) to the power of t