A quantity with an initial value of 160 grows continuously at a rate of 0.65% per hour. What is the value of the quantity after 402 minutes, to the nearest hundredth?

167.10

Step-by-step explanation:

Here, we write out the general form for an exponential equation;

y = I (1 + r)^n

where y is the current value which we want to calculate

I is the initial value which is 160

r is the growth rate = 0.65% = 0.65/100 = 0.0065

402 minutes to hours will be 402/60 = 6.7 hours which is n

Substituting these values, we have

y = 160( 1 + 0.0065)^6.7

y = 160(1.0065)^6.7

y = 167.10

Two possible answers are:

2/20 gallons per minute and 3/30 gallons per minute.

Explanation:

To find equivalent ratios, we are finding equivalent fractions.  To do this, we would multiply the numerator and denominator of the original fraction, 1/10, by the same constant.

(1*2)/(10*2) = 2/20 and (1*3)/(10*3) = 3/30.