A cup of coffee contains about 100mg caffeine. The exponential function A(t)=100(0.84)^t is used to calculate the amount of caffeine in a body t hours after the coffee was consumed. Find the amount of caffeine in the body after 4 hours. Can someone help with a step by step break down?
yeah. plug in the value for t and use your calculator:
A(4) = 100(0.84)^4 = 100*0.5 = 50.0
Sure! To find the amount of caffeine in the body after 4 hours using the given exponential function A(t)=100(0.84)^t, we can follow these steps:
Step 1: Substitute t = 4 into the given function to find A(4):
A(4) = 100(0.84)^4
Step 2: Simplify the exponent:
A(4) = 100(0.7056)
Step 3: Multiply to find the result:
A(4) = 70.56
Therefore, the amount of caffeine in the body after 4 hours is approximately 70.56mg.