You decide to start saving pennies according to the following pattern. You save 1 penny the first day, 2 pennies the second day, 4 the third day, 8 th

nicekikah

nicekikah

Answered question

2021-05-04

You decide to start saving pennies according to the following pattern. You save 1 penny the first day, 2 pennies the second day, 4 the third day, 8 the fourth day, and so on. Each day you save twice the number of pennies you saved on the previous day. Write an exponential function that models this problem. How many pennies do you save on the thirtieth day?

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-05-05Added 93 answers

Exponential functions are of the form y=a(b)^x when the initial amount a is when x=0 and of the form y=a(b)x1 where the intial amount is when x=1. For both forms, b is the growth or decay amount.
It is given that you save 1 penny on the first day so a= 1. The number of pennies you save doubles each day so the growth factor is b = 2. Since the initial amount is when x=1, then the equation will be of the form y=a(b)x1. Therefore, the number of pennies you save on day « is modeled by the equation y=2x1,
The number of pennies you save on the 30th day (x = 30) is then y=2301=229=536,870,912 pennies.

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