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Exponential Function Decay (Discrete) - Scenario to Equation

Level 1

This math topic focuses on modeling scenarios of exponential decay with discrete time steps using equations. The problems involve calculating the decay of populations, concentrations, and funds over time, given a constant percentage decline each period. Each problem includes a real-world situation, such as a declining bird or whale population, toxin reduction through dialysis, or the depletion of a charitable endowment, and asks to identify the correct exponential decay equation from multiple choices. This set of problems practices setting up and understanding exponential decay equations in contexts that model decreasing quantities over time.

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

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Exponential Function Decay (Discrete) - Scenario to Equation Worksheet

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Exponential Function Decay (Discrete) - Scenario to Equation
1
A bird population starts at 300. Each subsequent year it declines by 8%. After 7 years it has decreased to a population of 167.
Which equation describes this scenario?
a A LaTex expression showing 167 =700 times (1-0.08) to the power of (3)
b A LaTex expression showing 167 =300 times (1-0.08) to the power of (7)
c A LaTex expression showing 167 =800 times (1-0.03) to the power of (7)
2
A bird population starts at 900. Each subsequent year it declines by 2%. After 4 years it has decreased to a population of 830.
Which equation describes this scenario?
a A LaTex expression showing 830 =900 times (1-0.04) to the power of (2)
b A LaTex expression showing 830 =400 times (1-0.02) to the power of (9)
c A LaTex expression showing 830 =900 times (1-0.02) to the power of (4)
3
A whale population starts at 700. Each subsequent year it declines by 8%. After 3 years it has decreased to a population of 545 whales.
Which equation describes this scenario?
a A LaTex expression showing 545 =700 times (1-0.08) to the power of (3)
b A LaTex expression showing 545 =300 times (1-0.08) to the power of (7)
c A LaTex expression showing 545 =800 times (1-0.07) to the power of (3)
4
A toxin starts at a concentration of 400mg/L. Each daily dialysis reduces it by 7%. After 8 days it has decreased to a concentration of 223mg/L.
Which equation describes this scenario?
a A LaTex expression showing 223 =400 times (1-0.07) to the power of (8)
b A LaTex expression showing 223 =800 times (1-0.07) to the power of (4)
c A LaTex expression showing 223 =700 times (1-0.04) to the power of (8)
5
A charitable endowment starts with $300. Each daily it disburses 5% of its remaining funds. After 4 days its funds have decreased to $244.
Which equation describes this scenario?
a A LaTex expression showing 244 =300 times (1-0.05) to the power of (4)
b A LaTex expression showing 244 =500 times (1-0.03) to the power of (4)
c A LaTex expression showing 244 =400 times (1-0.05) to the power of (3)
d A LaTex expression showing 244 =300 times (1-0.04) to the power of (5)
6
A bird population starts at 400. Each subsequent year it declines by 7%. After 9 years it has decreased to a population of 208.
Which equation describes this scenario?
a A LaTex expression showing 208 =900 times (1-0.07) to the power of (4)
b A LaTex expression showing 208 =700 times (1-0.04) to the power of (9)
c A LaTex expression showing 208 =400 times (1-0.07) to the power of (9)
7
A toxin starts at a concentration of 600mg/L. Each hourly dialysis reduces it by 7%. After 5 hours it has decreased to a concentration of 417mg/L.
Which equation describes this scenario?
a A LaTex expression showing 417 =600 times (1-0.07) to the power of (5)
b A LaTex expression showing 417 =700 times (1-0.06) to the power of (5)
c A LaTex expression showing 417 =500 times (1-0.07) to the power of (6)
8
A whale population starts at 600. Each subsequent year it declines by 3%. After 5 years it has decreased to a population of 515 whales.
Which equation describes this scenario?
a A LaTex expression showing 515 =600 times (1-0.05) to the power of (3)
b A LaTex expression showing 515 =500 times (1-0.03) to the power of (6)
c A LaTex expression showing 515 =300 times (1-0.06) to the power of (5)
d A LaTex expression showing 515 =600 times (1-0.03) to the power of (5)