Question

The number of computers infected by a computer virus increases according to the model Vt) - 100e.^+67x, where to the time in hours. Find the number of computers infected after 1.5 hours, 2 hours, and 3 hours. (Round your answers to the nearest whole number) (a) 15 hours computers (b) 2 hours computers (c) 3 hours computers Neod Help? With

Answer 1

To find the number of computers infected after 1.5 hours, 2 hours, and 3 hours using the given model V(t) = 100e^(67t), where t is the time in hours, we can substitute the respective values and round the answers to the nearest whole number. Let's calculate:

(a) After 1.5 hours:

V(1.5) = 100e^(67 * 1.5)

= 100e^(100.5)

≈ 100 * 9.028761

≈ 902.8761

Rounded to the nearest whole number, the number of infected computers after 1.5 hours is approximately 903.

(b) After 2 hours:

V(2) = 100e^(67 * 2)

= 100e^(134)

≈ 100 * 2.57221 × 10^58 (a very large number)

Rounded to the nearest whole number, the number of infected computers after 2 hours is not meaningful as the value is extremely large.

(c) After 3 hours:

V(3) = 100e^(67 * 3)

= 100e^(201)

≈ 100 * 6.78343 × 10^87 (a very large number)

Rounded to the nearest whole number, the number of infected computers after 3 hours is not meaningful as the value is extremely large.

In conclusion, after 1.5 hours, approximately 903 computers will be infected. However, after 2 hours and 3 hours, the number of infected computers becomes too large to be expressed as a meaningful whole number.