Question

Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.

Abel: y = 1266.77(1.03)t

Zöe: y = 1159.27(1.03)t

Based upon this information, find the difference in the children’s ages.

Abel is ___ years older than Zöe.

Suggestions: Find the ratio 1266.77/1159.26. What does that ratio represent in terms of powers of 1.03? You also can graph both equations and figure out the shift.

Answer 1

Abel is 3 years older than Zoe.

Answer 2

Abel is 3 years older than Zöe.

Explanation:

Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.

Abel: y = 1266.77(1.03)^t

Zöe: y = 1159.27(1.03)^t

To find the difference in children's ages first we take ratio of 1266.77/1159.26

Ratio of 1266.77/1159.26= 1.09

now we write ratio in terms of powers of 1.03

1.03^t = 1.09

Take ln on both sides

t ln(1.03) = ln(1.09)

Divide both sides by ln(1.03)

t= 3

Abel is 3 years older than Zöe.