Provide an appropriate response.
-The population of a town with an initial population of 64,546 is decreasing at a rate of 3.7% per year. Create an exponential function of the form Q
$\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$
A) $\mathrm { Q } = 64,546 \times ( 1.037 ) ^ { \mathrm { t } }$
B) $Q = 64,546 \times ( 0.963 ) ^ { t }$
C) $Q = 64,546 \times ( - 2.7 ) ^ { t }$
D) $\mathrm { Q } = 64,546 \times ( 1.074 ) ^ { \mathrm { t } }$

Question

Provide an appropriate response.
-The population of a town with an initial population of 64,546 is decreasing at a rate of 3.7% per year. Create an exponential function of the form Q
 $\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$ 
A) $\mathrm { Q } = 64,546 \times ( 1.037 ) ^ { \mathrm { t } }$
B) $Q = 64,546 \times ( 0.963 ) ^ { t }$
C) $Q = 64,546 \times ( - 2.7 ) ^ { t }$
D) $\mathrm { Q } = 64,546 \times ( 1.074 ) ^ { \mathrm { t } }$

Quizplus · Accepted Answer

The correct formula for a decreasing population is $Q = Q_0 \times (1 - r)^t$, where $r$ is the rate of decrease. Since the population is decreasing by 3.7%, $r = 0.037$, and thus $1 - r = 0.963$. Therefore, the correct formula is $Q = 64,546 \times (0.963)^t$.

Provide an Appropriate Response Q=Q0×(1+r)t\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }Q=Q0​×(1+r)t

Provide an Appropriate Response $\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$