A quantity with an initial value of 3000 grows exponentially at a rate of 1.5% every 9 hours. What is the value of the quantity after 0.25 days, to the nearest hundredth?

3,029.56

Explanation:

Hi, to answer this, first, we have to calculate the percent increase per day:

Since the value grows exponentially at a rate of 1.5% every 9 hours, if we divide the rate by 9, we obtain the percent increase per hour.

1.5 /9 = 1/6% per hour

Since a day has 24 hours, by multiplying the hour increase by 24 we obtain:

1/6 x 24 = 4% per day

4% = 4/100 = 0.04 decimal form

Now, we have to apply exponential growth formula:

y = a (1+r )^x

Where:

a= initial value

r = growth rate

x = time interval

Replacing with the values given:

3000 ( 1 + 0.04)^x

solving for x = 0.25

3000 ( 1 + 0.04)^0.25 =3,029.56