Question

Two people at a university start a rumor, and now it is spreading throughout the university. The following function represents the number of people who have heard the rumor after h hours.

R(h)=2 × 10^(0.5h)
How many hours will it take for the rumor to be heard by 2,000 people?
A. 1.5
B. 6
C. 24
D. 12​

Answer 1

c. 24........,........

Answer 2

The answer is B. 6

R(h) is the number of people heard the rumor after h hour. For instance to find out how many people after to hour, put 2 in the place of the variable h. Let us do it: R(2) = 2 x 10^(0.5 x 2) , R(2) = 2 x 10^(1), R(2) = 20

Now, the question was to find what would be h when R(h) becomes 2,000

2,000 = 2 x 10^(0.5h)
2 x 10^3 = 2 x 10^(0.5h)
Now you can eliminate 2 on both sides
10^3 = 10^(0.5h)
Notice, in order the two sides to be equal, the exponents should be equal ( we know the bases on both sides are equal, 10)

Therefore: 3 = 0.5h, after h =3/0.5, h= 6