Solve the exponential equation below algebraically. Round your result to three decimal places. $250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000$
A) 86.873
B) 99.967
C) 111.803
D) 97.718
E) 87.344

Question

Quizplus · Accepted Answer

First, isolate the exponential term by dividing both sides by 250:

$$\frac{1.03^x}{0.03}=640$$

Next, multiply both sides by 0.03:

$$1.03^x=19.2$$

Then, take the logarithm (with any base) of both sides:

$$\log(1.03^x)=\log(19.2)$$

Use the power rule of logarithms to bring down the exponent:

$$x\log(1.03)=\log(19.2)$$

Solve for x by dividing both sides by $\log(1.03)$:

$$x=\frac{\log(19.2)}{\log(1.03)}\approx 99.967$$

Therefore, the answer is B, rounded to three decimal places.

Solve the Exponential Equation Below Algebraically 250[(1+0.03)x0.03]=160,000250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000250[0.03(1+0.03)x​]=160,000

Solve the Exponential Equation Below Algebraically $250 \left[ \frac { ( 1 + 0.03 ) ^ { x } } { 0.03 } \right] = 160,000$