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MathQuiz 4.2
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Exponentials - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following is the value of  e2   correct to 3 decimal places?
a) 7.389 .   b) 0.693 .
c) 5.437 .   d) 2.718 .

 

Your answer is correct.
Not correct. Choice (b) is false.
Try again, this is  ln2 .
Not correct. Choice (c) is false.
Try again, this is  2e .
Not correct. Choice (d) is false.
Try again, this is  e1.
Question 2 lion

Which of the following is the value of  e-2   correct to 3 decimal places?
a) -7.389 .
b) 0.736 .
c) 0.135 .
d) None of the above,  ex   is not defined for negative numbers.

 

Not correct. Choice (a) is false.
Try again, this is  - e2.   Remember  ex   is positive for all values of x.
Not correct. Choice (b) is false.
Try again, this is  2e-1.
Your answer is correct.
e- 2 = e12 = 0.135.
Not correct. Choice (d) is false.
Try again, there is a correct answer. The natural logarithm is not defined for negative numbers but the exponential function is.
Question 3 lion

Which of the following is the value of  2e3 + 4   correct to 3 decimal places?
a) 44.172 .   b) 44.171 .
c) 48.171 .   d) 6.197 .

 

Not correct. Choice (a) is false.
Try again, to calculate something to 3 decimal places you must use at least 4 decimal places in your working.
Your answer is correct.
2e3 + 4 = 2 × 20.0855+ 4 = 44.171.
Not correct. Choice (c) is false.
Try again, only the  e3   is multiplied by 2 .
Not correct. Choice (d) is false.
Try again, you have found 2 ln 3+ 4.
Question 4 lion

Which of the following solves  -2x e = 27   for x correct to 3 decimal places?
a) x = - 2.603.   b) x = 1.648.
c) x = - 4.966.   d) x = - 1.648.

 

Not correct. Choice (a) is false.
Try again, when solving find  ln 27   then divide by 2 .
Not correct. Choice (b) is false.
Try again, you seem to have lost a negative sign.
Not correct. Choice (c) is false.
Try again, you must take the natural log of both sides to solve this, not divide by  e.
Your answer is correct.
Correct, to solve this equation we take the natural log of both sides and ln27 - 2x = ln27 ⇒ x = - 2 = - 1.6479. Hence  x = - 1.648   correct to 3 decimal places.
Question 5 lion

Which of the following solves  2x+1 e = 15   for x correct to 3 decimal places?
a) x = 1.320 .   b) x = 1.946 .
c) x = 1.854.   d) x = 0.854.

 

Not correct. Choice (a) is false.
Try again, you must take the 1 away from ln15 , not from 15 .
Not correct. Choice (b) is false.
Try again, you must take the natural log of both sides before rearranging the equation.
Not correct. Choice (c) is false.
Try again, check your signs when solving the equation.
Your answer is correct.
To solve this equation we take the natural log of both sides and get
2x + 1 =ln 15
2x =ln 15- 1
x =ln15--1- 2.7081--1 2 = 2 = 0.85405.
Hence x = 0.854 correct to 3 decimal places.