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) Scenario to Starting Value

Level 1

This math topic focuses on solving exponential decay problems for an initial value, covering scenarios involving toxins, populations, and endowments. Problems entail calculating the starting concentration or population size after a certain percentage of decline over a given time period. Specific examples include determining the initial concentration of a toxin after monthly reductions, the initial funds in a charity endowment after monthly disbursements, and the initial sizes of bird and whale populations after annual percentage declines. The topic allows practice in translating real-world exponential decline scenarios into mathematical problems and solving for unknown initial values using exponential formulas.

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

more
WorksheetView

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

Mobius Math Academy logo
Exponential Function Solving - Decay (Discrete) Scenario to Starting ...
1
A toxin starts at a certain concentration. Each monthly dialysis reduces it by 8%. After 4 months it has decreased to a concentration of 214mg/L.
Solve for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = C over (1-r) to the power of t
b A LaTex expression showing 2 + C sub 0 = C times (1-r) to the power of t
c A LaTex expression showing 4 + C sub 0 = C over (1+r) to the power of t
d A LaTex expression showing 9 + C sub 0 = C times (1-r) to the power of t
2
A charitable endowment starts with a certain amount of money. Each monthly it disburses 2% of its remaining funds. After 6 months its funds have decreased to $442.
Solve for the starting cash given this scenario?
a A LaTex expression showing 1 + 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
d A LaTex expression showing 9 + P sub 0 = P times (1-r) to the power of t
3
A bird population starts at a certain size. Each subsequent year it declines by 2%. After 3 years it has decreased to a population of 376.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 7 + P sub 0 = P over (1+r) to the power of t
c A LaTex expression showing 0 + P sub 0 = P over (1+r) to the power of t
d A LaTex expression showing 5 + P sub 0 = P over (1+r) to the power of t
4
A whale population starts at a certain size. Each subsequent year it declines by 7%. After 6 years it has decreased to a population of 129 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 3 + P sub 0 = P times (1-r) to the power of t
b A LaTex expression showing 8 + P sub 0 = P times (1-r) to the power of t
c A LaTex expression showing 7 + P sub 0 = P times (1-r) to the power of t
d A LaTex expression showing P sub 0 = P over (1-r) to the power of t
5
A whale population starts at a certain size. Each subsequent year it declines by 6%. After 2 years it has decreased to a population of 441 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 4 + P sub 0 = P over (1+r) to the power of t
b A LaTex expression showing 9 + 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
6
A whale population starts at a certain size. Each subsequent year it declines by 9%. After 5 years it has decreased to a population of 187 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 4 + 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 8 + P sub 0 = P times (1-r) to the power of t
d A LaTex expression showing 9 + P sub 0 = P over (1+r) to the power of t
7
A toxin starts at a certain concentration. Each hourly dialysis reduces it by 8%. After 3 hours it has decreased to a concentration of 155mg/L.
Solve for the starting concentration given this scenario?
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 over (1+r) to the power of t
c A LaTex expression showing 7 + C sub 0 = C over (1+r) to the power of t
d A LaTex expression showing 7 + C sub 0 = C times (1-r) to the power of t
8
A bird population starts at a certain size. Each subsequent year it declines by 8%. After 7 years it has decreased to a population of 278.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over (1-r) to the power of t
b A LaTex expression showing 4 + P sub 0 = P over (1+r) to the power of t
c A LaTex expression showing 9 + P sub 0 = P over (1+r) to the power of t