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

72 fudge and 75 toffee

step-by-step explanation:

i hope this : )

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~