Write an inequality that represents `t`, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning

Question:

At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.

Write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning.

Step-by-step explanation:

Given

Let T = temperature and t = hours past midnight

So, we have:

--- at midnight

--- rate (it is negative because the temperature drops)

Required

Determine the inequality when the temperature is colder than -4 degrees

First, we calculate the hours when the temperature at -4 degrees

This is represented as:

Using the slope formula, we have:

Solve for t

This implies that: at 4.5 hours, the temperature is at -4 degrees Celsius.

So, the inequality is:

l.jnl.j/n.m,lm,

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for