Initial Amount: 12 Rate of Growth: 5 % Value of the Function when t=5: ≈ 15.3
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.
y=12(1.05)^t ⇔ y= 12(1+ 0.05)^t
Our function represents exponential growth, with an initial amount a= 12 and a rate of growth r= 0.05. To rewrite the rate of growth as a percent, we move the decimal point two places to the right.
r=0.05 ⇔ r=5 %
Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula.
<deduct>
y=12(1.05)^t
t= 5
y=12(1.05)^{{\color{#0000FF}{5}}}
expand Evaluate right-hand side
Calculate power
y=12(1.276281\ldots)
Multiply
dnapxe
y=15.315378\ldots
Round to 1 decimal place(s)
y\approx15.3
</deduct>
