Exponential Function Growth (Continuous) - Meaning to Term

Level 1

This math topic focuses on understanding the components of exponential function growth in continuous settings. It includes identifying terms such as the final population, growth rate, initial amounts, and final amounts across different real-world scenarios including population growth, social media post views, app downloads, savings account growth, and share prices. The problems predominantly require identifying which part of the exponential function equation (final value, rate of growth, or initial value) corresponds to a particular aspect of a scenario described. Each problem utilizes typical exponential growth models expressed mathematically as $ P = P_0 \times e^{(r \times t)} $, where $ P_0 $ is the starting value, $ r $ is the rate, and $ P $ represents the value after time $ t $.

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Exponential Function Growth (Continuous) - Meaning to Term Worksheet

Exponential Function Growth (Continuous) - Meaning to Term

In this model of continuous growth of a rabbit population, which term represents the final population?

$A LaTex expression showing P =P sub 0 times e to the power of (r times t) \\\text{final population} = ?$

In this model of continuous exponential growth of social media post views, which term represents the rate?

$A LaTex expression showing V =V sub 0 times e to the power of (r times t) \\\text{rate} = ?$

In this model of continuously compounding growth of app downloads, which term represents the starting downloads?

$A LaTex expression showing A =A sub 0 times e to the power of (r times t) \\\text{starting downloads} = ?$

In this model of continuously compounding growth of money in a savings account, which term represents the final cash?

$A LaTex expression showing P =P sub 0 times e to the power of (r times t) \\\text{final cash} = ?$

$A LaTex expression showing P =P sub 0 times e to the power of (r times t) \\\text{starting population} = ?$

In this model of continuous growth of a rabbit population, which term represents the starting population?

$A LaTex expression showing P =P sub 0 times e to the power of (r times t) \\\text{rate} = ?$

In this model of continuous growth of a bacteria population, which term represents the rate?

In this model of continuously compounding growth of a share price, which term represents the final price?

$A LaTex expression showing S =S sub 0 times e to the power of (r times t) \\\text{final price} = ?$

In this model of continuously compounding growth of a share price, which term represents the starting price?

$A LaTex expression showing S =S sub 0 times e to the power of (r times t) \\\text{starting price} = ?$