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 (Continuous) Scenario to Starting Value

Level 1

This math topic involves solving exponential decay problems in continuous scenarios to determine the starting value of a population or concentration. The problems entail calculating initial sizes of whale, bird, bacteria populations, and toxin concentrations, given their decline rates (percent per quarter, day, or year) and final measurements after a specified period. Skills practiced include understanding exponential functions, interpreting word problems, and applying mathematical principles to real-world contexts. The exercise integrates algebraic manipulation focusing on exponential decay formulas.

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

more
WorksheetView

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

Mobius Math Academy logo
Exponential Function Solving - Decay (Continuous) Scenario to Startin...
1
A whale population starts at a certain size. It declines continuously at 4% per quarter. After 9 quarters it has decreased to a population of 418 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 9 + P sub 0 = \frac{e to the power of (-r times t) }{P}
b A LaTex expression showing 4 + P sub 0 = P over e to the power of (\frac{-r {t )}}
c A LaTex expression showing 6 + P sub 0 = P over e to the power of (\frac{-r {t )}}
d A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
2
A bird population starts at a certain size. It declines continuously at 8% per quarter. After 5 quarters it has decreased to a population of 201.
Solve for the starting population given this scenario?
a A LaTex expression showing 3 + P sub 0 = P over e to the power of (\frac{-r {t )}}
b A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
c A LaTex expression showing 8 + P sub 0 = P over e to the power of (\frac{-r {t )}}
3
A bacteria population starts at a certain size. It declines continuously at 4% per day. After 6 days it has decreased to a population of 157 bacteria.
Solve for the starting population given this scenario?
a A LaTex expression showing 3 + P sub 0 = P over e to the power of (\frac{-r {t )}}
b A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
c A LaTex expression showing 1 + P sub 0 = P over e to the power of (\frac{-r {t )}}
d A LaTex expression showing 6 + P sub 0 = P over e to the power of (\frac{-r {t )}}
4
A whale population starts at a certain size. It declines continuously at 8% per quarter. After 7 quarters it has decreased to a population of 228 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 8 + P sub 0 = P over e to the power of (\frac{-r {t )}}
b A LaTex expression showing 8 + P sub 0 = \frac{e to the power of (-r times t) }{P}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
d A LaTex expression showing 5 + P sub 0 = \frac{e to the power of (-r times t) }{P}
5
A whale population starts at a certain size. It declines continuously at 8% per quarter. After 9 quarters it has decreased to a population of 194 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing 4 + P sub 0 = P over e to the power of (\frac{-r {t )}}
b A LaTex expression showing 8 + P sub 0 = P over e to the power of (\frac{-r {t )}}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
d A LaTex expression showing 6 + P sub 0 = P over e to the power of (\frac{-r {t )}}
6
A toxin starts at a certain concentration. It declines continuously at 6% per day. After 3 days it has decreased to a concentration of 751mg/L.
Solve for the starting concentration given this scenario?
a A LaTex expression showing 7 + C sub 0 = C over e to the power of (\frac{-r {t )}}
b A LaTex expression showing 8 + C sub 0 = \frac{e to the power of (-r times t) }{C}
c A LaTex expression showing C sub 0 = C over e to the power of (-r times t)
7
A whale population starts at a certain size. It declines continuously at 4% per year. After 7 years it has decreased to a population of 604 whales.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
b A LaTex expression showing 7 + P sub 0 = \frac{e to the power of (-r times t) }{P}
c A LaTex expression showing 2 + P sub 0 = P over e to the power of (\frac{-r {t )}}
d A LaTex expression showing 3 + P sub 0 = \frac{e to the power of (-r times t) }{P}
8
A bird population starts at a certain size. It declines continuously at 9% per quarter. After 7 quarters it has decreased to a population of 213.
Solve for the starting population given this scenario?
a A LaTex expression showing 7 + P sub 0 = \frac{e to the power of (-r times t) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
c A LaTex expression showing 2 + P sub 0 = P over e to the power of (\frac{-r {t )}}
d A LaTex expression showing 1 + P sub 0 = P over e to the power of (\frac{-r {t )}}