Answer:
[TeX]f(t)=80*2^{t-1} [/TeX]
f(10)=40960 people
Step-by-step explanation:
The number of people who have heard the rumour doubles every day.
If on the first day, 80 people have heard,
On the Second day, 160 persons would have heard.
This is an example of an exponential sequence whose growth ratio is 2.
The nth term of an exponential sequence is derived using the formula:
[TeX]U_n=ar^{n-1} [/TeX]
Where:
a=first term
r=growth ratio.
In this case, a=80, r=2
Therefore:
At any time t, the number who would have heard the rumor is:
[TeX]f(t)=80*2^{t-1} [/TeX]
(b)In 10 days,
[TeX]f(10)=80*2^{10-1} [/TeX]
[TeX]=80*2^{9} [/TeX]
=40960
In 20 days, 40960 persons would have heard the rumor.
