Question

Jackson purchases a new car for $48,000. The car's value can be modeled by the
following exponential function: y = 48000(0.76)^t where y represents the car's
value and t represents time in years. What is the decay rate expressed as a
percentage? *

Answer 1

We have been given that Jackson purchases a new car for $48,000. The car's value can be modeled by the  following exponential function: $y = 48000(0.76)^t$ where y represents the car's  value and t represents time in years. We are asked to find the decay rate as a percentage.

We know that an exponential decay function is in form $y=a\cdot (1-r)^x$, where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form,

x = time.

Upon comparing our given function $y = 48000(0.76)^t$ with standard decay function  $y=a\cdot (1-r)^x$, we can see that $1-r=0.76$.

Let us solve for r.

$1-1-r=0.76-1$

$-r=-0.24$

$r=0.24$

Let us convert 0.24 into percentage.

$0.24\times 100\%=24\%$

Therefore, the decay rate is 24%.