Exponential Function Growth (Continuous) - Scenario to Equation

Level 1

This math topic focuses on formulating equations based on scenarios involving exponential growth modeled by continuous functions. Each problem describes real-world situations where quantities such as population, downloads, views, or savings accounts grow continuously over time, defined by constant percentage rates and specific time frames. Learners are tasked with identifying the correct equation representing each scenario, where the exponential function is typically expressed using the base 'e' (Euler's number). These problems aid in understanding how exponential growth can be applied and calculated in everyday contexts.

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

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Exponential Function Growth (Continuous) - Scenario to Equation Worksheet

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Exponential Function Growth (Continuous) - Scenario to Equation
1
An app starts with 800 downloads. Its download count grows continually by 5% each week.After 9 weeks it has 1,254 downloads.
Which equation describes this scenario?
a A LaTex expression showing 1,254 =800 times e to the power of (0.05 times 9)
b A LaTex expression showing 1,254 =500 times e to the power of (0.08 times 9)
c A LaTex expression showing 1,254 =900 times e to the power of (0.05 times 8)
2
A bacteria population starts at 200. It grows continuously at 3% growth per month. After 7 months it has increased to a population of 246.
Which equation describes this scenario?
a A LaTex expression showing 246 =200 times e to the power of (0.07 times 3)
b A LaTex expression showing 246 =700 times e to the power of (0.03 times 2)
c A LaTex expression showing 246 =200 times e to the power of (0.03 times 7)
d A LaTex expression showing 246 =300 times e to the power of (0.02 times 7)
3
A bacteria population starts at 200. It grows continuously at 7% growth per day. After 5 days it has increased to a population of 283.
Which equation describes this scenario?
a A LaTex expression showing 283 =700 times e to the power of (0.02 times 5)
b A LaTex expression showing 283 =200 times e to the power of (0.07 times 5)
c A LaTex expression showing 283 =500 times e to the power of (0.07 times 2)
4
An insect population starts at 300. It grows continuously at 7% growth per year. After 4 years it has increased to a population of 396.
Which equation describes this scenario?
a A LaTex expression showing 396 =700 times e to the power of (0.03 times 4)
b A LaTex expression showing 396 =300 times e to the power of (0.04 times 7)
c A LaTex expression showing 396 =400 times e to the power of (0.07 times 3)
d A LaTex expression showing 396 =300 times e to the power of (0.07 times 4)
5
A social media post starts with 400 views. Its view count grows continually by 7% each year.After 6 years it has 608 views.
Which equation describes this scenario?
a A LaTex expression showing 608 =600 times e to the power of (0.07 times 4)
b A LaTex expression showing 608 =400 times e to the power of (0.07 times 6)
c A LaTex expression showing 608 =400 times e to the power of (0.06 times 7)
6
A bacteria population starts at 400. It grows continuously at 2% growth per month. After 3 months it has increased to a population of 424.
Which equation describes this scenario?
a A LaTex expression showing 424 =400 times e to the power of (0.02 times 3)
b A LaTex expression showing 424 =300 times e to the power of (0.02 times 4)
c A LaTex expression showing 424 =400 times e to the power of (0.03 times 2)
7
A savings account starts with $900. It grows continuously at 8% interest per year. After 4 years it has $1,239.
Which equation describes this scenario?
a A LaTex expression showing 1,239 =900 times e to the power of (0.08 times 4)
b A LaTex expression showing 1,239 =800 times e to the power of (0.09 times 4)
c A LaTex expression showing 1,239 =400 times e to the power of (0.08 times 9)
8
An app starts with 200 downloads. Its download count grows continually by 8% each week.After 7 weeks it has 350 downloads.
Which equation describes this scenario?
a A LaTex expression showing 350 =700 times e to the power of (0.08 times 2)
b A LaTex expression showing 350 =800 times e to the power of (0.02 times 7)
c A LaTex expression showing 350 =200 times e to the power of (0.08 times 7)