exponential functions\nthe number of text messages sent per student each month is growing by 17% per year…

exponential functions\nthe number of text messages sent per student each month is growing by 17% per year. if the current number is 400 per month, what will the number be in 7 years?\ny = (1+ )

exponential functions\nthe number of text messages sent per student each month is growing by 17% per year. if the current number is 400 per month, what will the number be in 7 years?\ny = (1+ )

Answer

Explanation:

Step1: Identify the growth formula components

The exponential growth formula is ( y = a(1 + r)^t ), where ( a ) is the initial amount, ( r ) is the growth rate (in decimal), and ( t ) is the time. Here, the initial number ( a = 400 ).

Step2: Convert the growth rate to decimal

The growth rate is ( 17% ), so ( r = \frac{17}{100} = 0.17 ).

Step3: Determine the time ( t )

The time period ( t = 7 ) years.

Step4: Fill in the formula

Substitute ( a = 400 ), ( r = 0.17 ), and ( t = 7 ) into the formula ( y = a(1 + r)^t ). So we get ( y = 400(1 + 0.17)^7 ).

Answer:

The first blank is ( 400 ), the second blank is ( 0.17 ), and the third blank is ( 7 ). So the formula is ( y = \boldsymbol{400}(1 + \boldsymbol{0.17})^{\boldsymbol{7}} ).