Question
The amount remaining of a 195
mL sample of a liquid substance, y
(in mg) after x
hours is modeled by y=1951+0.025e0.09x
where x≥0
.
To the nearest tenth of an hour, how long will it take for the substance to decay from 187
mL to 185
mL?
mL sample of a liquid substance, y
(in mg) after x
hours is modeled by y=1951+0.025e0.09x
where x≥0
.
To the nearest tenth of an hour, how long will it take for the substance to decay from 187
mL to 185
mL?
Answers
GPT-4o mini
To solve for the time it takes for the substance to decay from 187 mL to 185 mL using the given formula
\[
y = 195 \cdot 1 + 0.025 e^{0.09x}
\]
we first need to find the values of \( x \) for when \( y = 187 \) and \( y = 185 \).
1. Setting \( y = 187 \):
\[
187 = 195 + 0.025 e^{0.09x}
\]
Now, we can rearrange this equation:
\[
187 - 195 = 0.025 e^{0.09x}
\]
\[
-8 = 0.025 e^{0.09x}
\]
Since a negative amount cannot be represented by this exponential function, it's clear that the given model may not be valid for values beyond 195 mL. Ensure you have the accurate decay model. Given the current model, finding negative concentrations makes it unfeasible. Thus, check your values or model.
As we recognize this inconsistency in the model, let's make adjustments to derive getting reliable metric values generally needed.
Assuming a new model describes decay typically, we may fit or verify the model against available decay data. Please clarify if alternate models based on actual experimental decay data were used.
\[
y = 195 \cdot 1 + 0.025 e^{0.09x}
\]
we first need to find the values of \( x \) for when \( y = 187 \) and \( y = 185 \).
1. Setting \( y = 187 \):
\[
187 = 195 + 0.025 e^{0.09x}
\]
Now, we can rearrange this equation:
\[
187 - 195 = 0.025 e^{0.09x}
\]
\[
-8 = 0.025 e^{0.09x}
\]
Since a negative amount cannot be represented by this exponential function, it's clear that the given model may not be valid for values beyond 195 mL. Ensure you have the accurate decay model. Given the current model, finding negative concentrations makes it unfeasible. Thus, check your values or model.
As we recognize this inconsistency in the model, let's make adjustments to derive getting reliable metric values generally needed.
Assuming a new model describes decay typically, we may fit or verify the model against available decay data. Please clarify if alternate models based on actual experimental decay data were used.