Math Problem Statement

Enter the function P = 5e^(-2.6t) in the form P = P0 * a^t. Does the function represent exponential decay or exponential growth?

Solution

Let's break down the given function P=5e−2.6tP = 5e^{-2.6t} and convert it into the desired form P=P0atP = P_0 a^t.

  1. The original function is:
    P=5e−2.6tP = 5e^{-2.6t} Comparing this with the form P=P0atP = P_0 a^t, we know P0=5P_0 = 5. Now, we need to express the exponential base e−2.6te^{-2.6t}

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Algebra

Formulas

P = P0 * a^t
P = P0 * e^(kt)

Theorems

Exponential Decay Formula

Suitable Grade Level

Grades 9-12

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