Initial Amount: 0.5 Rate of Growth: 25 % Value When t=3: ≈ 0.2
Practice makes perfect
Let's start by recalling the general formulas for exponential growth and exponential decay functions.
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Exponential Growth & Exponential Decay [0.8em]
y=a(1+r)^t & y=a(1-r)^t
In both cases, a>0 is the initial amount and r>0 is the rate of growth or decay written in decimal form. Moreover, for exponential decay, r is less than 1. Let's rewrite the given function to match one of the above formulas.
Our function represents exponential decay, with an initial amount a= 0.5 and a rate of decay r= 0.25. To rewrite the rate of decay as a percent, we move the decimal point 2 places to the right.
r=0.25 ⇔ r=25 %
Finally, to evaluate the function when t=3 we will substitute 3 for t in the given formula.
<deduct>
y=0.5\left(\dfrac{3}{4}\right)^t
t= 3
y=0.5\left(\dfrac{3}{4}\right)^{{\color{#0000FF}{3}}}
