Question

ch. 9.4 homework - day 1 for each question below, determine which of the exponential equations you will use. then write the equation that represents the scenario and use it to find the missing value. 1) a company promises to release a new smartphone model every month. each model’s battery life will be 5% longer than the previous model’s. if the current model’s battery life is 737 minutes, what will the latest model’s battery life be 7 months from now? exponential growth (simple interest) $a = p(1 + r)^t$ exponential decay $a = p(1 - r)^t$ circle: growth / decay equation: $p =$ $r =$ $t =$ battery life 7 months from now:

Explanation:

Step1: Identify the type of exponential model

Since the battery life is increasing by 5% each month, this is an exponential growth scenario. So we use the exponential growth formula \( A = P(1 + r)^t \).

Step2: Determine the values of P, r, and t

• \( P \) (initial value) is the current battery life, so \( P = 737 \) minutes.
• \( r \) (growth rate) is 5% or \( 0.05 \) (since 5% = \( \frac{5}{100}=0.05 \)).
• \( t \) (time in months) is 7.

Step3: Substitute the values into the formula

Substitute \( P = 737 \), \( r = 0.05 \), and \( t = 7 \) into \( A = P(1 + r)^t \):
\[
A = 737(1 + 0.05)^7
\]

Step4: Calculate \( (1 + 0.05)^7 \)

First, calculate \( 1.05^7 \). Using a calculator, \( 1.05^7\approx1.4071 \).

Step5: Calculate A

Multiply 737 by \( 1.4071 \):
\[
A\approx737\times1.4071\approx1037.03
\]

Answer:

• Circle: Growth
• Equation: \( A = 737(1 + 0.05)^t \)
• \( P = 737 \), \( r = 0.05 \), \( t = 7 \)
• Battery life 7 months from now: Approximately 1037.03 minutes