Question

the function $m(t)=7210 \cdot 1.015^{t}$ represents the amount of money in a savings account as a function of time.
the a-value is type your answer... which represents the choose your answer...
the b-value is type your answer... meaning that the function choose your answer... by type your answer... %.
5 fill in the blank 16 points
the function $b(t)=500 \cdot 1.004^{t}$ represents the number of bacteria in a petri dish as a function of time.
the a-value is type your answer... which represents the choose your answer...
the b-value is type your answer... meaning that the function choose your answer... by type your answer... %
6 fill in the blank 17 points
the function $v(t)=32,000 \cdot 0.96^{t}$ represents the value of a new car as a function of time.
the a-value is type your answer... which represents the choose your answer...
the b-value is type your answer... meaning that the function choose your answer... by type your answer... %

Explanation:

For $M(t) = 7210 \cdot 1.015^t$

Step1: Identify initial amount (a-value)

Exponential form: $M(t)=a \cdot b^t$, $a=7210$

Step2: Interpret a-value

Represents initial savings account amount

Step3: Identify growth factor (b-value)

$b=1.015$

Step4: Calculate growth rate

$\text{Rate}=(1.015-1) \times 100 = 1.5\%$, function grows

For $B(t) = 500 \cdot 1.004^t$

Step1: Identify initial amount (a-value)

Exponential form: $B(t)=a \cdot b^t$, $a=500$

Step2: Interpret a-value

Represents initial bacteria count

Step3: Identify growth factor (b-value)

$b=1.004$

Step4: Calculate growth rate

$\text{Rate}=(1.004-1) \times 100 = 0.4\%$, function grows

For $V(t) = 32000 \cdot 0.96^t$

Step1: Identify initial value (a-value)

Exponential form: $V(t)=a \cdot b^t$, $a=32000$

Step2: Interpret a-value

Represents initial car value

Step3: Identify decay factor (b-value)

$b=0.96$

Step4: Calculate decay rate

$\text{Rate}=(1-0.96) \times 100 = 4\%$, function decays

Answer:

1. For $M(t) = 7210 \cdot 1.015^t$:

• The a-value is $\boldsymbol{7210}$ which represents the initial amount of money in the savings account
• The b-value is $\boldsymbol{1.015}$ meaning that the function grows by $\boldsymbol{1.5}$%

1. For $B(t) = 500 \cdot 1.004^t$:

• The a-value is $\boldsymbol{500}$ which represents the initial number of bacteria
• The b-value is $\boldsymbol{1.004}$ meaning that the function grows by $\boldsymbol{0.4}$%

1. For $V(t) = 32000 \cdot 0.96^t$:

• The a-value is $\boldsymbol{32000}$ which represents the initial value of the new car
• The b-value is $\boldsymbol{0.96}$ meaning that the function decays by $\boldsymbol{4}$%