Initial Amount: 6.72 Rate of Growth: 100 % Value When t=5: ≈ 215.0
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 growth r is more than 1. Let's rewrite the given function to match one of the above formulas.
Our function represents exponential growth, with an initial amount a= 6.72 and a rate of growth r= 1. To rewrite the rate of growth as a percent, we move the decimal point two places to the right.
r=1 ⇔ r=100 %
Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula.
<deduct>
g(t)=6.72(2)^t
t= 5
g({\color{#0000FF}{5}})=6.72(2)^{{\color{#0000FF}{5}}}
expand Evaluate right-hand side
Calculate power
g(5)=6.72(32)
Multiply
dnapxe
g(5)=215.04
Round to 1 decimal place(s)
g(5)\approx 215.0
</deduct>
