Approximate the solution to the equation 20=125ex

Question

by locating the intersection point of y=125ex
and y=20
.(1 point)
Responses

x≈125
x approximately equals 125

x≈20
x approximately equals 20

x≈−1.8
x approximately equals negative 1.8

x≈1.8

Answer 1

To approximate the solution to the equation \( 20 = 125 e^x \), we can start by rearranging it into a more manageable form:

\[ e^x = \frac{20}{125} \]

Calculating the right side:

\[ \frac{20}{125} = 0.16 \]

Now, taking the natural logarithm of both sides, we have:

\[ x = \ln(0.16) \]

Calculating \( \ln(0.16) \):

\[ x \approx -1.832 \]

So, the approximate value of \( x \) is \( -1.8 \).

Therefore, the correct response is:

x ≈ -1.8 (x approximately equals negative 1.8)