Question

expressing exponential models as lo
lesson posttest
question 11 points 4
solve the equation $9e^{2.1x} - 5 = 12.2$.
note: use your own words to answer this question.

Explanation:

Step1: Isolate the exponential term

Add 5 to both sides of the equation \(9e^{2.1x}-5 = 12.2\) to get \(9e^{2.1x}=12.2 + 5\).
Simplify the right - hand side: \(9e^{2.1x}=17.2\).

Step2: Solve for the exponential term

Divide both sides of the equation \(9e^{2.1x}=17.2\) by 9. We have \(e^{2.1x}=\frac{17.2}{9}\approx1.9111\).

Step3: Take the natural logarithm of both sides

Take the natural logarithm of both sides of the equation \(e^{2.1x}\approx1.9111\). Using the property \(\ln(e^{a})=a\), we get \(\ln(e^{2.1x})=\ln(1.9111)\), which simplifies to \(2.1x=\ln(1.9111)\).

Step4: Solve for x

Divide both sides of the equation \(2.1x=\ln(1.9111)\) by 2.1. We know that \(\ln(1.9111)\approx0.648\), so \(x=\frac{\ln(1.9111)}{2.1}\approx\frac{0.648}{2.1}\approx0.309\).

Answer:

\(x\approx0.309\)