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Home » \( x = -\frac32 \). - ClickBalance

\( x = -\frac32 \). - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Thus, the diameter of the circle is \(17\) cm, so the radius is \(8.5\) cm. The circumference \(C\) is:

📌 C = 2\pi r = 2\pi \times 8.5 = 17\pi \text{ cm}

📌 The circumference of the circle is \(\boxed{17\pi}\) cm.**Question:

📌 A herpetologist studying the conservation of endangered reptiles and amphibians in Southeast Asia models the population growth of a rare species using the equation \( P(t) = P_0 e^{rt} \), where \( P_0 \) is the initial population, \( r \) is the growth rate, and \( t \) is time in years. Given \( P_0 = 100 \), \( r = 0.05 \), and \( P(t) = 200 \), solve for \( t \).

📌 We start with the equation for population growth:

📌 \[ P(t) = P_0 e^{rt} \]

📌 Given values are \( P_0 = 100 \), \( r = 0.05 \), and \( P(t) = 200 \). Plug these into the equation:

📌 \[ 200 = 100 e^{0.05t} \]

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