Question

A rumor spreads through a group of teenagers

Answer 1

Answer:

a). N = 2

b). N = 16

c). t = 624 minutes

Step-by-step explanation:

Exponential model that shows the rumor spread through a group is

$N=2(1.81)^{0.7t}$

Where N = Number of teenagers who have heard the rumors

t = Duration after the rumor first started

(a). At the time t = 0

$N=2(1.81)^{(0.7\times 0)}$

N = 2

Therefore, 2 teenagers started the rumor.

(b). At t = 5 hours

N = $2(1.81)^{0.7\times 5}$

N = 15.96

N ≈ 16

16 teenagers heard the rumors after 5 hours.

(c). If N = 150

150 = $2(1.81)^{0.7t}$

75 = $(1.81)^{0.7t}$

log(75) = 0.7t(log1.81)

1.87506 = 0.7t(0.25767)

t = $\frac{1.87506}{0.180369}$

t = 10.395 hours

t ≈ 624 minutes

Therefore, after 624 minutes or rumor will be heard by 150 teenagers.