Question

HelP MeEe
A virus that initially infected four people is spreading at a rate of 15% each week. The following function represents the weekly spread of the virus: f(x) = 4(1.15)x. Rewrite the function to show how quickly the virus spreads each day and calculate this rate as a percentage.

f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily

f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily

f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily

f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily

Answer 1

Answer:

f(x) = 4(1.02)^(7x); spreads at a rate of approximately 2% daily

Step-by-step explanation:

The weekly number of people infected is:

f(x) = 4(1.15)^x

So the daily number of people infected is:

f(x) = 4(1+r)^(7x)

To find the value of the daily rate r, we set this equal to the first equation.

4(1.15)^x = 4(1+r)^(7x)

(1.15)^x = (1+r)^(7x)

(1.15)^x = ((1+r)^7)^x

1.15 = (1+r)^7

1.02 = 1+r

r = 0.02

So the equation is f(x) = 4(1.02)^(7x), and the daily rate is approximately 2%.

Answer 2

Using exponential functions, it is found the daily function for the spread is:

$f(x) = 4\left(\frac{1.15}{7}\rigth)^{x}$, and it spreads at a rate of approximately 2% daily.

An exponential function has the following format:

$y = ab^x$

In which:

• a is the initial value.
• b is the rate of change.

In this problem, the function for the weekly spread is:

$f(x) = 4(1.15)^x$

A week has 7 days, thus, to find the daily spread, we divide the rate of change by 7, that is:

$f(x) = 4\left(\frac{1.15}{7}\right)^x$

$\frac{15}{7} \approx 2.1$, thus, it spreads at a rate of approximately 2% daily.

A similar problem is given at https://brainly.com/question/23416643