The population of Lavender Hills (in tens) can be modeled with the following equation, where 𝑡t represents the years since 19501950. Graph the exponential function, rounding to the nearest integer whenever necessary.

𝑝(𝑡)=82(1.07)𝑡

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2468101214−2−4−6−8−10−12−1420406080100120140




Here is the graph of the population of Lavender Hills, based on the equation \( p(t) = 82(1.07)^t \). The population increases exponentially, starting from 82 (in tens) in 1950 and growing to about 142 (in tens) after 14 years.

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Here are 5 questions to expand on this topic:
1. How does the growth rate affect the shape of the exponential graph?
2. What would happen to the population if the growth rate increased to 10%?
3. How would the graph change if the initial population were different, say 100?
4. What is the doubling time of this population, and how can it be calculated?
5. How would the graph look if the population were decreasing instead of growing?

**Tip:** Exponential functions grow faster over time as the rate of increase is proportional to the current value.

The population of Lavender Hills (in tens) can be modeled with the following equation, where t represents the years since 1950. Graph the exponential function, rounding to the nearest integer whenever necessary.

p(t) = 82(1.07)^t

Learn how to graph the population growth of Lavender Hills using the exponential function p(t) = 82(1.07)^t. This problem involves key mathematical concepts like exponential growth, graphing, and population modeling. Suitable for students in Grades 9-12.

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