When Parker left his house this morning, his cell phone was 20% charged and it then started to lose 4% charge for each hour thereafter. Write an equation for B, commaB, in terms of t, commat, representing the charge remaining in Parker's battery, as a percentage, tt hours after Parker left his house.
B = 20 - 4t
To write an equation for B in terms of t, we can use the information given.
Initially, Parker's cell phone had a charge of 20%, which means the initial value, B₀, is 20.
The cell phone loses 4% charge for each hour, so the rate of change, r, is -4.
Since we're looking for the charge remaining in Parker's battery, we can represent this as a percentage, B(t).
Therefore, the equation for B in terms of t is:
B(t) = B₀ + r * t
Substituting the given values:
B(t) = 20 + (-4) * t
Simplifying:
B(t) = 20 - 4t
Hence, the equation representing the charge remaining in Parker's battery, as a percentage, tt hours after leaving his house, is B(t) = 20 - 4t.
To write the equation for the charge remaining in Parker's battery as a percentage, we need to consider the initial charge and the rate at which it decreases.
Let's start with the initial charge, which is given as 20%. This can be represented as 0.20 in decimal form.
Next, we need to consider the rate at which the battery charge decreases. It is stated that the battery loses 4% charge for each hour. This means for each hour, the battery charge decreases by 4%.
To represent the decrease in charge over time, we multiply the rate of decrease by the number of hours, which is represented by 't'.
So, after 't' hours, the battery charge would decrease by 4% multiplied by 't', which can be expressed as 0.04t in decimal form.
To find the remaining charge, we subtract the rate of decrease from the initial charge:
B = 0.20 - 0.04t
Therefore, the equation for the remaining battery charge, 'B', as a percentage after 't' hours is B = 0.20 - 0.04t.