Question

Did I do something wrong? I multiplied by 1.02 six times and got a realllllly ugly decimal.

Rebecca runs a quarter-mile each week. In each of the last 6 weeks her time has improved (decreased) by 2%, and she can now run a quarter-mile in 66 seconds. What was her time six weeks ago?

Answer 1

75 seconds

Explanation:

Here, we want to get her time 6 weeks ago.

We shall have an exponential model to link this all up

The exponential model would look like;

y = I(1 - r)^n

where y is the present time

I is the initial time she started with which we are calculating

r is the rate of change which is 2% = 2/100 = 0.02

n is the week number which is 6 in this case

So we have;

66 = I(1 - 0.02)^6

66 = I(0.98)^6

I = 66/0.8858

I = 74.5 seconds

This is approximately 75 seconds

Her time 6 weeks ago is 75 seconds