The exponential function y(x)=Ceαx satisfies the conditions y(0)=2 and y(1)=1. (a) Find the constants C and α. Enter the exact value of α. Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin(2x) or (a−b)/(1+n).

a = -0.6931471806

C = 2

Step-by-step explanation:

Given that y(x) = Ce^(ax) satisfies the conditions y(0) = 2, and y(1) = 1.

We need to find the values of a and C.

To do this, we are going to apply the conditions given to the function y(x), this way, we will obtain two equations which can then be solved simultaneously.

Applying y(0) = 2, put y(x) = 2 and x = 0 in y(x) = Ce^(ax)

2 = Ce^(a × 0)

C = 2 (because e^0 = 1)(1)

Again, applying y(1) = 1, put y = 1 and x = 1 in y(x) = Ce^(ax)

1 = Ce^(a × 1)

Ce^a = 1 (2)

From (1), C = 2. Putting this in (2), we have

2e^a = 1

Divide both sides by 2

e^a = 1/2

This equation has an index which could make finding a prove difficult by a direct mean, to find a, we need to take logarithm of both sides,

log(e^a) = log(1/2)

(a)log(e) = log(1/2)

a = log(1/2)/(log e)

a = (-0.3010299957)/(0.4342944819)

a = -0.6931471806

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

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the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

answer: 100

step-by-step explanation: