Exponential, logarithmic, and logistic functions Quiz 1

Question 1

Arun found a set of functions in his workbook and got confused about which function is an exponential function. Help him to find which of the following is$$/$$are exponential function

Accepted Answer

$$h\left( x \right)={{x}^{5/2}}$$

Answer

$$f\left( x \right)=5{{e}^{-4x}}$$

Answer

$$g\left( x \right)={{2}^{x/4}}$$

Answer

$$w\left( x \right)=\dfrac{17}{{{7}^{x}}}$$

Question 2

If $${{\log }_{4}}a-2{{\log }_{64}}a=3{{\log }_{a}}4$$. Then find $$a$$.

Accepted Answer

Both (a) and (b)

Answer

$$64$$

Answer

$$\dfrac{1}{64}$$

Answer

None of the above.

Question 3

If there is an equation as $${{\log }_{4}}(x+6)={{\log }_{4}}(x-6)+2{{\log }_{4}}2$$, then find $$x$$.

Accepted Answer

10

Answer

-10

Answer

11

Answer

25

Question 4

Kiran found an interesting equation in a book that is $${{20}^{{{\log }_{17}}289}}+{{15}^{{{\log }_{16}}256}}=576+{{\log }_{7}}x$$. So that he wants to find the variable in that equation. What is the value that Kiran wants?

Accepted Answer

$${{7}^{49}}$$

Answer

$${{7}^{48}}$$

Answer

$${{7}^{50}}$$

Answer

None of the above.

Question 5

There is an experiment to find the population of bacteria. It is given that the population growth of bacteria is in the equation as $$f(t)=\dfrac{9000}{1+{{e}^{-0.15(t-18)}}}$$. Find out how many years it will take to get the population of bacteria to 6000? $$($$Round off the result to whole number$$)$$

Accepted Answer

23

Answer

19

Answer

22

Answer

20