Question

Suppose a rumor is spreading that eating pickles will raise a​ person's IQ. Assume that 80 people have heard the rumor as of today and each day the number of people​ (past and​ present) who have heard it doubles. Let​ f(t) be the number of people​ (past and​ present) who have heard the rumor at t days since today.
a. Find an equation of f.
b. How many American (past and Present will have heard the rumor in 10 days from now)

Answer 1

Answer:

$f(t)=80*2^{t-1}$

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:

$U_n=ar^{n-1}$

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:

$f(t)=80*2^{t-1}$

(b)In 10 days,

$f(10)=80*2^{10-1}$

$=80*2^{9}$

=40960

In 20 days, 40960 persons would have heard the rumor.