Solve the problem.
-If the function $Q ( t ) = 4 e ^ { - 0.00938 t }$ models the quantity (in $\mathrm { kg }$ ) of an element in a storage unit after $t$ years, how long will it be before the quantity is less than $1.5 \mathrm {~kg}$ ? Round to the nearest year.
A) $105 \mathrm { yr }$
B) $31 \mathrm { yr }$
C) $45 \mathrm { yr }$
D) $4 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find when the quantity is less than 1.5 kg, set $Q(t) < 1.5$ and solve for $t$:$$4e^{-0.00938t} < 1.5$$Divide both sides by 4:$$e^{-0.00938t} < \frac{1.5}{4}$$$$e^{-0.00938t} < 0.375$$Take the natural logarithm of both sides to solve for $t$:$$-0.00938t < \ln(0.375)$$$$t > \frac{\ln(0.375)}{-0.00938}$$$$t > 104.72$$Rounding to the nearest year, it will be 105 years before the quantity is less than 1.5 kg.

Solve the Problem Q(t)=4e−0.00938tQ ( t ) = 4 e ^ { - 0.00938 t }Q(t)=4e−0.00938t

Solve the Problem $Q ( t ) = 4 e ^ { - 0.00938 t }$