Question

Find the exponential function that satisfies the given conditions: Initial value = 64, decreasing at a rate of 0.5% per week

Answer 1

Answer:

Step-by-step explanation:

An exponential function is of the form

$y=ab^x$

where a is the initial value and b is the growth/decay rate.  Our initial value is 64.  That's easy to plug in.  It goes in for a.  So the first choice is out.  Considering b now...

If the rate is decreasing at .5% per week, this means it still retains a rate of

100% - .5% = 99.5%

which is .995 in decimal form.

b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1.   .995 is less than 1 so it is a rate of decay.  The exponential function is, in terms of t,

$f(t) = 64(.995)^t$