Question

Scientists are modeling the spread of a virus that affects tomato plants. According to their model, 34 plants are infected on day 0, and the virus infects 1% more plants each day.
What type of function could describe the relationship between the number of plants infected, f(x), and the day x?
Write an equation for f(x). If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.
f(x)=

Answer 1

The scenario describes a growth in the number of infected plants where the number of infections increases by 1% each day. This indicates exponential growth.

In mathematical terms, when something grows by a percentage each day, it can be represented by an exponential function.

Given:
- Initial number of infected plants (on day 0) = 34
- Daily growth rate = 1% = 0.01

The general formula for an exponential growth function can be represented as:
\[
f(x) = a(b)^x
\]
Where:
- \(a\) is the initial amount (the value at day 0),
- \(b\) is the growth factor (1 + growth rate),
- \(x\) is the number of days.

For this scenario:
- \(a = 34\)
- \(b = 1 + 0.01 = 1.01\)

Thus, the function that describes the number of infected plants after \(x\) days is:
\[
f(x) = 34(1.01)^x
\]

This equation indicates that the number of infected tomato plants grows exponentially at a rate of 1% each day.