If y= 2e^0.3x when y= 1.6 find x
Substitute y=1.6 into the equation and solve for x:
y=2e^(0.3x)
1.6=2e^(0.3x)
0.8=e^(0.3x)
ln(0.8)=0.3x
ln(0.8)/0.3=x
x=-0.7438118377
0.8 = e^0.3x
ln 0.8 = 0.3 x
-0.223 = 0.3 x
To find the value of x when y is equal to 1.6, we can substitute the given values into the equation and solve for x.
Given:
y = 1.6
y = 2e^(0.3x)
Substituting y = 1.6 into the equation:
1.6 = 2e^(0.3x)
To isolate the exponential term, divide both sides of the equation by 2:
1.6/2 = e^(0.3x)
Simplifying the left side of the equation:
0.8 = e^(0.3x)
To solve for x, we can take the natural logarithm (ln) of both sides:
ln(0.8) = ln(e^(0.3x))
Since ln(e^(0.3x)) is equivalent to 0.3x, the equation becomes:
ln(0.8) = 0.3x
Now, divide both sides of the equation by 0.3 to solve for x:
ln(0.8)/0.3 = x
Using a calculator or a math software, we can evaluate the left side of the equation:
x ≈ -0.5365
Therefore, when y is equal to 1.6, x is approximately -0.5365.
To find the value of x when y is equal to 1.6, we can substitute y = 1.6 into the equation y = 2e^(0.3x) and then solve for x.
Here's how to do it step by step:
Step 1: Substitute y = 1.6 into the equation. We have:
1.6 = 2e^(0.3x)
Step 2: Divide both sides of the equation by 2 to isolate the exponential term:
0.8 = e^(0.3x)
Step 3: Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential term:
ln(0.8) = ln(e^(0.3x))
Step 4: We can simplify the equation using the logarithmic property that ln(e^a) = a:
ln(0.8) = 0.3x
Step 5: Divide both sides of the equation by 0.3 to solve for x:
x = ln(0.8) / 0.3
Step 6: Use a calculator to evaluate the right side of the equation to find the value of x:
x ≈ -0.384
Therefore, when y = 1.6, x is approximately -0.384.